There are two things that I can think could happen if done before assembly.
Scratching a piece then having to restain. You may end up with a spot that the stain is a little darker that the rest. But then again staining it tight corners is tough and the same may occur when you push hard to make contact.
If you have pieces that are a tight fit applying a finish before assembly may make it too tight for aeembly. Or, the fit you get is different from the one prior to finishing.
For what it’s worth I think most people finish after assembly but there is nothing wrong with staining a piece that will become hard to do if assembled first. Staining would have less of an impact when done prior to assembly. It’s up to you.