You can but is there any point? It will not speed up the listing if and when the site is reviewed and found to meet our criteria. It will tell you if it has been rejected but not why (policy). It will tell you if it has been moved to another category. You would be better off forgetting it, maybe checking the category every so often to see if it has been listed, but focusing your efforts elsewhere - if it ever gets listed it will be a bonus but contrary to popular misconception it will not suddenly turn your business into a super-performer - if all listed and unreviewed sites were taken together that would make a pile of 50,000 web designers, which equals a fair few search engine pages and makes you a fairly small needle in a haystack.
I can't see which part of New York you are in, but if you find the locality category in the Regional branch for your neighbourhood/town you can suggest the site there as well without it impacting on the existing suggestion.