I can't say for sure, but my guess is probably yes. Both install scripts want to install the full web stack in their own way. If you install FusionPBX first, Vesta might override nginx settings so that it can manage them. If FusionPBX is installed afterward, it'll overwrite anything Vesta has setup. And, depending on how Vesta manages those settings, it might not see the settings that FusionPBX has added and overwrite them or ignore them.
Now, that's if you use their respective install scripts. If you install VestaCP first (and make sure to grab the PostgreSQL stuff as stated in the Vesta docs), you should be able to only install some parts from the fusionpbx install script. It's all just bash so you can install the pieces that won't break VestaCP (such as freeswitch) and set up the remaining pieces manually (like your virtual host, iptables, and fail2ban).
Not a perfect solution, but it's something.