If the threshold has been reached, it's highly unlikely there would be any sort of delay to announcing that until after the by-elections. Parliament is in recess at the moment, and with Boris Johnson essentially on official engagements over this weekend, Graham Brady would no doubt use that as the reasoning for not speaking to the PM yet. But convention dictates that he should speak to him as soon as practicable if those letters have hit that magic number (in Theresa May's case, he waited for her to get back from abroad). There was talk of MPs holding off putting letters in pending the by-election results, but if reports are to be believed the numbers have been hit now
If they have the numbers, then Brady would advise Johnson and discuss when the vote should take place - usually the night before a public announcement. When Theresa May faced a no confidence vote in December 2018, the threshold being hit was announced just before 8am and the vote was held that same evening. I can't see there being much of a wait for a vote in this case either, which is why there's been reports of phone calls taking place to MPs in the past week or so - for one reason to get people to withdraw letters, another to try to preempt that vote and encourage people to vote for confidence in him. When the whole process is getting such heavy coverage in the media, there's little benefit to be gained in delaying the vote.
There's already far too much damaging stuff about him swirling around in the media, so my gut feeling would be that the "best" case option for him is to push for a vote as quickly as possible. The only good option for him is to have the vote, win and that protects him from a further challenge for 12 months. Of course, Theresa May only knows all too well that winning a confidence vote doesn't mean you stay in power. Her confidence vote which she won then progressed into a vote of no confidence motion laid in Parliament in January, and her subsequent resignation announcement in March - a mere 3 months after the 1922 committee vote.
This is a leader that's pretty much in terminal decline now, and my view that it's a case of when, rather than if he goes still stands. I can't see him leading the next election, it's just whether the Tories want to get rid and attempt to recover now, or get rid closer to the next election when the damage done could be far more substantial, but an option for a new leader becomes more obvious.