The counter to this is that its not a particularly old convention, and that Boris and mad Liz already did plenty of topping up for the last parliament.It is quite normal for the Leader of the Opposition to nominate peers at the routine topping-up times and it would be a considerable breach of convention for Starmer not to put Johnson forward if he is nominated in such a situation. However, the Appointments Commision could object to Johnson’s nomination and it would be unusual (although not unknown: see Cruddas above) to push it through against their objection. Sunak has the right to nominate peers when leaving office and I suspect that these are in the system at the moment: it would be interesting to see if he has nominated Johnson and what happens if the Commission says no.
Given that the Lords is widely accepted to be very overlarge and is already stacked with Tories, and that part of the Labour manifesto was to make inroads into that, I don't think it would be very controversial to say to Sunak that he only gets three.
Looked at another way, it was widely assumed that the queen personally blocked Blair for a long time, so it's not impossible that Charles would personally object to that dreadful oik.
Short answer is that there are loads of blocks to having him in the shadow cabinet, but he probably wouldn't fancy that job anyway. He would be a lot easier to slot in whenever they won an election, with an advance promise that that was how it would be done