Not in my experience, the only time this group will thing really makes a big difference is during the construction of the mana body and this is correlated to it’s ability to hold mana/animus.
There have been a lot of groups that have severely wished for a demon lord to wither away and die, but they don’t. If they notice, they usually in fact get ticked off and start slaughtering said individuals.
Now…on the other hand…gods do seem subject to this affect…in that their power is directly related to how many worshipers they have.
I have no evidence that this affects them directly/personally, but their relative power on a given plane is dependent on the number of worshipers and their belief.
For example, I have seen instances where on one plane a particular deity is a major god, but on other planes he/she is a minor god.
Not sure how this works, at all.