Possible. Between the time Sonny dies and Michael returns, I would imagine that Tom was at the height of his power. I would imagine that he ran most of the day to day operateions and spared Vito the trouble of dealing with anything other than "need to know" issues.
I agree that it's a possible scenario. But there could be a different interpretation:
When Tom told Vito that Sonny'd been killed, Vito said: "This war ends now...I want you to arrange a meeting with the heads of the Five Families..." So, Vito got off his sick bed and got back in charge as soon as Sonny was gone. And his first action was to ask for a truce--to alleviate the pressure on the Family, and to prepare for getting Michael home. A
possible inference is that Vito knew Tom could not carry the family forward without Sonny or himself in charge. Another is that, although Vito knew Sonny was "a bad Don," he may have held Tom in some way negligent in Sonny's assassination.
With Vito off his sick bed, I'm guessing Tessio and Clemenza gravitated back to him. Tom may have, as you suggest, done some filtering of the issues that Vito had to decide. But I think Tom's greatest influence was with Sonny--and it diminished when Sonny died.
