Addendum

Now that this writeup has a Rep of -2, I figured that it was time to go find a non-flippant answer to this question, lest more "We are not amused" monks find the need to vote--.

I've spent about 15 minutes looking for where it actually spells out that Anonymous Monks do not gain experience, and I've come up with nada.

However, if one looks at Anonymous Monk, one will note that this user has not received any experience despite the fact that he/she/it has, at the time of this writing, 981 writeups.

Therefore, one can reasonably ass-u-me that an Anonymous Monk cannot receive experience within the current configuration of perlmonks.

Conversely, it is within the realm of the possible (but improbable) that this may change in the future.

In conclusion, I refer any future voters to the top of this writeup for the answer to Just for fun could Anonymous Monk gain XP?