Of course, he is. The scene is a picture and a foreshadow of the adoption of the gentiles, as sons of God, through the cross. What we have here is Jacob with his hands crossed on his grandsons, accepting them as his own sons.
Let me point out that according to the halakha those two boys would be considered gentiles today. And a few verses earlier, Israel said:
15 And he blesses Joseph and says, “God, before whom my fathers
Abraham and Isaac habitually walked: God who is feeding me from my
being to this day: 16 the Messenger who is redeeming me from all evil
blesses the youths, and my name is called on them, and the name of my
fathers Abraham and Isaac; and they increase (דָּגָה dagah) into a
multitude in the midst of the land.”
H1711. dagah
Meaning: to spawn, become numerous
A primitive root; to move rapidly; used only as a denominative from dag;
And what does dag mean in Hebrew? Fish. One of the earliest and the most universal symbols of Christianity.
Yes, the Septuagint has plethos ethnon rather than pleroma ton ethnon, but it is close. And the Strong's Concordance states that the Hebrew equivalent of pleroma is indeed melo:
Corresponding Greek / Hebrew Entries: - מְלֹא (melo, Strong's H4393): Often translated as "fullness" or "that which fills," used in contexts such as the fullness of the earth or the fullness of time.
https://biblehub.com/greek/4138.htm
The name Ephraim is often used by the Old Testament writers as a code word representing the whole Ten Northern Tribes of Israel. No other author uses that name more often than Hosea. In chapters 1 and 2, he repurposes Deuteronomy 32:21. The verse originally talking about gentiles is used in the context of the Ten Northern Tribes. Then both Paul (in Romans 9), and Peter (in 1 Peter 2:10) quote Hosea in the context of the gentiles again.
They have made Me zealous by 'no-god,' They made Me angry by their
vanities; And I make them zealous by 'no-people (לֹא-עָם lo am),' By a
foolish nation I make them angry. (Deuteronomy 32:21)
2 The commencement of Jehovah’s speaking by Hosea. And Jehovah saith
unto Hosea, ‘Go, take to thee a woman of whoredoms, and children of
whoredoms, for utterly go a-whoring doth the land from after Jehovah.’
3 And he goeth and taketh Gomer daughter of Diblaim, and she
conceiveth and beareth to him a son; 4 and Jehovah saith unto him,
‘Call his name Jezreel, for yet a little, and I have charged the blood
of Jezreel on the house of Jehu, and have caused to cease the kingdom
of the house of Israel; 5 and it hath come to pass in that day that I
have broken the bow of Israel, in the valley of Jezreel.’ 6 And she
conceiveth again, and beareth a daughter, and He saith to him, ‘Call
her name Lo-Ruhamah, for I add no more to pity the house of Israel,
for I do utterly take them away; 7 and the house of Judah I pity, and
have saved them by Jehovah their God, and do not save them by bow, and
by sword, and by battle, by horses, and by horsemen.’ 8 And she
weaneth Lo-Ruhamah, and conceiveth, and beareth a son; 9 and He saith,
‘Call his name Lo-Ammi (לֹא עַמִּי), for ye [are] not My people, and I
am not for you; 10 and the number of the sons of Israel hath been as
the sand of the sea, that is not measured nor numbered, and it hath
come to pass in the place where it is said to them, Ye [are] not My
people, it is said to them, Sons of the Living God; (Hosea 1)
19 And I have betrothed thee to Me to the age, And betrothed thee to
Me in righteousness, And in judgment, and kindness, and mercies, 20
And betrothed thee to Me in faithfulness, And thou hast known Jehovah.
21 And it hath come to pass in that day, I answer — an affirmation of
Jehovah, I answer the heavens, and they answer the earth. 22 And the
earth doth answer the corn, And the new wine, and the oil, And they
answer Jezreel. 23 And I have sowed her to Me in the land, And I have
pitied Lo-Ruhamah, And I have said to Lo-Ammi (לֹא עַמִּי), My people
thou [art], and it saith, My God!’ (Hosea 2 )
21 Or does the potter not have authority over the clay, to make out of
the same lump one vessel unto honor, but one unto dishonor? 22 And
what if God, desiring to show the wrath and to make known His power,
bore with much patience the vessels of wrath, having been fitted for
destruction, 23 that He might also make known the riches of His glory
upon the vessels of mercy, which He prepared beforehand for glory, 24
even us, whom He has called not only out from the Jews, but also out
from the Gentiles? 25 As He also says in Hosea: “I will call that
which is not My people, My people; and her not having been loved,
having been loved,” 26 and, “It will happen that in the place where it
was said to them, ‘You are not My people,’ there they will be called
‘sons of the living God.’” (Romans 9)
9 But you are a chosen race, a royal priesthood, a holy nation, a
people for His possession, so that you may proclaim the excellencies
of the One having called you out of darkness into His marvelous light
[Peter alludes to Isaiah 9:1-2], 10 who once were not a people, but
now are the people of God; those not having received mercy, but now
having received mercy. (1 Peter 2)
As for the last part of your question, what those people teach is a complete nonsense. The Israel of God is build on faith not ethnicity. The lost sheep of Israel are the believing gentiles, like the Canaanite woman of Matthew 15. Paul was the apostle to the nations.
26 And He made from one man every nation of men, to dwell upon all the
face of the earth, having determined the appointed times and the
boundaries of their habitation, 27 to seek God, if perhaps indeed they
might palpate for Him, and might find Him. And indeed, He is not far
from each one of us. 28 ‘For in Him we live and move and are.’ As also
some of the poets among you have said, ‘For we are also His
offspring.’ 29 Therefore, being offspring of God, we ought not to
consider the Divine Being to be like to gold or to silver or to stone,
a graven thing of man’s craft and imagination. 30 So indeed God,
having overlooked the times of ignorance, now commands all men
everywhere to repent, 31 because He set a day in which He is about to
judge the world in righteousness by a man whom He appointed, having
provided a guarantee to all, having raised Him out from the dead.”
(Acts 17)
God also promised Abram in Genesis 12:3, that in him (his seed) all the families of the earth would be grafted. The root of the word ונברכו is the same as that of מבריך, “to graft.”
