Not so far as I know. Most obviously affected would be fanfilms. According to people close to Phase II, they have a specific liason at CBS/Paramount who deals with the topic, and she is pretty good at letting them know what they can and cannot do (such as the prohibition on them selling their costumes, props, etc or openly soliciting donations with PayPal accounts, etc).
Phase II did
have one run in with CBS/Paramount over the unproduced TOS script "He Walked Among Us", which they wanted to produce. The studio said "no". The situation was resolved amicably.