Would calling for a new election (late May/early June perhaps) "stop the clock" on a possible VoNC?
Or is the process of going thru a VoNC completely separate from the dissolution of Parliament?
So its complicated.
The Vote of No Confidence process requires the existance of the 1922 Committee of backbench Tory MPs. When parliament is dissolved then people are no longer MPs automatically which may automatically dissolve that committee and end the term of the chair; so there may be no one present to call an election. In any case it would require Conservatives to have a vote and I suspect mid-election no one would want that for quite obvious reasons - so people publicly calling for it would probably find themselves losing Conservative backing in the election at that point.
However Lascelles Principles (which guide the thinking of the palace around requests to dissolve) include a provision that if the palace think there's someone else that could command the confidence of the house they would decline a dissolution. This is designed for Hung Parliament situations where confidence votes might naturally lead to government changing (the precedent on this was the King/Byng affair in Canada which admittedly did not end well - but it is an example of testing parliament before an early election) but its believed that if Sunak went to the palace between the VoNC being announced and it being held the Palace would decline until the vote happens: as then the question would be around if the Conservative Party would choose someone new to command the confidence of the House. if he was confirmed in the party then that wouldn't be a problem even if he won by one vote as the assumption would be that the party would unite around him until proven otherwise. I guess there's theoretically a window in the wash-up period (the days between the PM calling an election and parliament formally being prorogued; where basically the big two parties hash out deals on what legislation both agree should get through parliament before the election, and what needs to be dropped) where they could change leader; but then I wonder if the Palace would delay accepting the PMs resignation until after an election as he'd be a caretaker in any case.
So to summarise: he probably has the power to pre-empt a confidence vote if they haven't gotten to the formal point of triggering it yet (as at that point he would theoretically be the only person that could command the confidence of the house; as there is no other rival leader or official challenge) and that calling of an election would stall procedings; while if Brady announced a Confidence Vote tomorrow he could not go to the palace immediately after and call an election because his position as the only person that could govern with the confidence of the house is challenged.