I’ve done a couple of Q3 test maps in Max, export to ASE, caulk hull in radiant, autoclip… I still can’t decide whether it’s worth pursuing doing a full map that way. The potential to destroy any chances of being able to BSP the map due to their being billions of unique planes on the autoclip brushes for something like the average cave is scary. In Q3 I found bots getting stuck in completely unlikely places (standing turning on the spot in the middle of a relatively flat floor). Although possibly the main reason I’ve not really pursued it is that I hate UVing stuff 
Collision iffiness could easily arise because the Max model won’t have all its vertices on the grid unless you’ve been exceptionally anal about it during construction (which throws away the potential speed advantages you get by making your less regular geometry in a high-end app). When you compile I think the autoclipping will try to put everything on grid like GTKR does, hence a mismatch. My first test maps had glitchy bits you could get stuck on, the second had triangles that didn’t seem to get clips generated. You could usually fix these by moving some verts around.
You could do a map in Max, but it would need a lot more testing and fixing for even relatively simple geometry. And it’ll generally be a much bigger BSP than an equivalent brush based map. Although you can compile your ASE with autoclip, decompile the BSP and manually optimise the clip brushes. Tried this too, it gets boring quick 