He's just as much allowed to nominate himself as any other member can nominate themselfs. so No but then again he's an admin so he could do it if he would like to
Members are not allowed to nominate themselves:
Per the Rules
1) Nominations are to begin on Mondays.... unless otherwise specified. Please DO NOT begin the Nominting until then. You can nominate up to 2 Member's Signatures. The nominated Sig(s) must be one that is being used by that member, at the time of your nomination. Previously awarded Sigs are also ineligible. Be sure to say why that/those particular Signature(s) are worthy of your nomination(s). Please DO NOT nominate yourself, let other members evaluate your work and nominate you accordingly.