If you are just using the app on your phone, you should not have any issues with custom ROMs.
If you are looking to use the online service: there isn't quite as simple of an answer, but any stable ROMs should work 100% with Pulse SMS.
Pulse SMS depends heavily on Google Play Services to provide push notifications from the web/backend to your device. The custom ROM must have Google Play Services set up, to work. Without them, Pulse SMS wouldn't be able to send from the web, and the service would be useless.
So, if the custom ROM has some Google Play Services issues, then the online service will not work for you.