Basswood is technically a hardwood (though it's physically quite soft), so it should respond in a similar way to other hardwoods. I've seen people do shellac finishes on basswood with no problems.
Finish thickness is not normally an issue with fitting components. The only area to be careful of is the neck pocket. This is normally left unfinished, with just maybe 2mm of the very inside edges having finish applied, to help the finish stick to the sharp pocket corners. The neck itself is finished all over (except for maybe the fretboard, which some people simply wax rather than add a clear coat).
One thing to check before starting any finishing is to check the bridge positioning. You need to do a mock build. this is described in the instruction manual you can download from this web page.
https://www.pitbullguitars.com/instruction-manual/
A lot of the TL kits need the bridge pickup rout extended in order to position the bridge so the intonation can be correctly set once it's all put together. This is something that can be done with a Dremel drum sander bit and some care.