Well the answer is "it depends". There are a number of things to consider:
If the page is high traffic then it might not matter that irrelevant posts are made. They'll be outnumbered by the on topic posts so people won't necessarily spot them. They'll be there for people to seek out, but they won't be "in your face".
If the page is low traffic then while they might keep people coming back to the page, there's a real danger that they'll overwhelm the real posts and people will miss those.
If the community is serious (by that I mean intent of discussing the topic in hand) then the irrelevant posts will be seen as a distraction and won't be welcomed.
However, if the community is more frivolous then they might well welcome them as long as they are somewhat related to the fan page's subject.
If serious, on-topic posts can be pinned or otherwise highlighted then the frivolous stuff might be OK as it won't crowd out the things people are there to discuss.
If there's a way for people to hide or ignore threads then this might be a way to allow the frivolous to be an opt-outed of. For example, if you can tag posts and people can ignore specific tags then this would give you the best of both worlds.
You need to take all these things into consideration and, most importantly, have a discussion within your community to see if you should allow the irrelevant stuff or not. You also might need to periodically revisit the discussion if circumstances change - for example if the irrelevant stuff seems like it might be taking over and actually driving people away.