On balance the mods probably do get a higher ratio of likes to their posts then average, but not necessarily more then the most popular posters. If we take likes as being an objective measure of popularity this needn't be any evidence of "sucking up". On the contrary, it's almost certainly part and parcel of the reason they were selected in the first place.
Remember that first and foremost they are posters, posters who have at some point been deemed suitable of a little extra responsibility.
By definition that requires their posting be consistently above par for the areas they moderate and thus likely to be generating above average likes anyway.
Chicken and the egg....
Does being a mod gain you sycophantic likes or does being a strong poster gain you a mod position?
The "most likes" list puts
@Locutus of Bored (a mod)at number one, but
@BillJ (a regular user) comes third with a similar ratio of likes to posts.
@{ Emilia } is second place for total score but again ratio wise plenty of non mods match her at the 60% ball park. I've no doubt there are people getting closer to parity, although I've not the time to sit and poke around right now.
So yes some mods do get more than the average number of likes, but not to the extent that it cannot be explained by strong posting or, for that matter, matched by non moderating posters