No.
As already noted in the question and in this answer, the bonusebonuses granted by this magic rod are onregard spell attacks rolls and saving throw DCs of warlock'warlock's spell.
Note that if your table allows multiclassing and you have levels in another class with a spellcasting feature, these bonuses do not apply to the rolls and DCs related to this class.
When a magic item grants bonus to a weapon attacks and/or damage, it states so.
There are magic items which are not weapons that grant such kind of bonus. A not comprehensive list includes:
[...] you gain a +2 bonus to damage rolls on ranged attacks made with such weapons.
[...] For 1 hour, the coated item is magical and has a +3 bonus to attack and damage rolls.