Not particularly. The only real use of the UNSC presidency powers so far was to attempt to hold the February 21st Security Council session, held at the request of Ukraine and sponsored by several UNSC members, in private. However, this was overruled by a council vote, and the session was held in public.
The President also presides over the meetings, calling representatives in turn and can issue rulings on points of order raise, but these rulings may be challenged by the council and put to a vote.
Ukraine’s representative was referring to rule 20 of the provisional rules of procedure, which states:
Whenever the President of the Security Council deems that for the proper fulfillment of the responsibilities of the presidency he should not preside over the Council during the consideration of a particular question with which the member he represents is directly connected, he shall indicate his decision to the Council. The presidential chair shall then devolve, for the purpose of the consideration of that question, on the representative of the member next in English alphabetical order, it being understood that the provisions of this rule shall apply to the representatives on the Security Council called upon successively to preside. This rule shall not affect the representative capacity of the President as stated in rule 19, or his duties under rule 7.
So even if Russia had agreed to stand down, it would have only affected that session of the Council, and the presidency would be retained. As a permanent member of the Council, Russia retains veto power over any substantive resolutions anyway, so the very minor powers available to it through holding the rotating presidency seem relatively negligible.