It's definitely worth forming. The AI won't get a significant amount of culture from it. The AI usually don't have a lot of cities, therefore don't have a lot of trade routes and it's unlikely that they will send all to your cities, if any, so most of the culture they will get on your alliance will come from your trade routes, which isn't a lot (1 culture per trade route). You also need to consider that just because the AI didn't do a cultural alliance with you, it doesn't mean they won't do a cultural alliance, so by avoiding an alliance you're hurting yourself without actually preventing the AI from having a cultural alliance, quite the opposite, if you're not one of the members of the Alliance, another AI is. When you make an alliance, you prevent that leader from making that same alliance with another leader, which might mean one less AI with a cultural alliance.
Meanwhile, the tier 2 cultural alliance is amazing for cultural since it give you more great people points on your districts. Send a trade route to your cultural alliance from every city with a theater square for a significant boost.You can also make the alliance with a leader that isn't doing well culturally. Even if the culture the AI get from the alliance was significant, it's only a problem if your ally is the leader with highest domestic tourists count. If you're boosting a leader that isn't doing well, the extra culture they are getting won't change how much visiting tourists you need since it won't be enough to set them as the leader with highest domestic tourists count.
The only significant culture bonus from alliance is the tier 3 bonus but that come too late to matter and also give you a tourism boost. As I just explained, it won't be a problem if your ally isn't the leader with more domestic tourists, so even if you get to that tier 3, you can prevent it from hurting you just by making an alliance with a leader with low culture.