I don't know if it would be a serious mark against you, but, as a general rule, if a program "strongly recommends" something (as do some of the programs I have applied to in the past or am planning on applying to for this upcoming cycle), I would probably follow their advice and submit anything that they took the time to so explicitly note as important.
Also, if you get a really good score on it, it's just another chance to show them how strong of a candidate you are compared to those who have significantly lower scores on it, those who did not submit their scores, and those who did not take the test at all.
I know it may be slightly cost and time prohibitive, but, honestly, the psych GRE is actually pretty easy. Just get a good intro to psych textbook and a study guide (e.g. Kaplan) and you should be more than fine.