Ahhhh, the age old question. This is really one only you can answer, how far do you want to go and are you up to the task? It is way less nerve racking to put the drive train in first and not have to worry about that fresh paint on the outside. But the biggest pain is keeping it from getting overspray all over it. You most certainly want the outside completely finished, blocked, ready for a quick sand and paint. But even then it is very difficult to keep that undercarriage free of overspray and sanding dust. But realistically it's the best way to go unless you are making an out and out show car. You can keep it perfectly clean as you do the outside but it's another bit of work to add to the project.
But assembling it all painted isn't out of the question in the least bit.
You won't be painting the underside and the top side at the same time anyway (that is a HUGE undertaking shooting them both at once) so doing the underside then putting the drive train in makes a lot of sense on your typical build.