No, don't do this. The problem with your proposed circuit is that as soon as the two neutral paths are connected at the fan, you no longer control which neutral carries how much return current. The two cables connected at the fan are almost sure to carry unbalanced current.
You can do what you want safely, and prepare for future installation of powered smart switches, but not strictly according to current NEC. You have to wire one way today, then potentially change it around later to accommodate smart switches. It's possible without running any more cables.
With mechanical switches, you want to abandon the run from the basement light to the first 3-way by capping it off at the switch box. (You will use this cable again if you convert to smart switches.) Repurpose the white wires between the fan and the switches to be always-hot, making this run a bog-standard 3-way switch loop:
With smart switches, you will abandon the run from the other basement light to the fan (the "new 12/2"), and reconnect the cable from the first basement light. Depending on the type of smart switch, you may also no longer need the red wire between the switches:
Note: I would never do this in somebody else's house. I would do it in my own house, but I would document it and add it to my "technical debt" list in the "ordinance conformance" section.