No.
And some reasons....
1. No evidence it will make any difference over 8 or 9 games, which is all he'd get, things could get worse and we might finish outside the top 4.
2. No evidence that he even works with the first team squad anyway, and therefore might not have any idea what is required for number 1.
3. No evidence that he can manage this standard/level of player.
4. He's already got a job, which in my view is on an equal to the first team coach, and we shouldn't disrupt that, as it may be more important to the long term strategy of the club than losing to Burnley.
5. Some (many) of the players need a kick up the arse, and I doubt they would be willing to take it from PV, he might have been a hard man as a player, and might be highly respected for that, but there's no sign of either as a coach, yet.
6. The club has a strategy that is working, there will always be peaks and troughs, this is a trough, no need to panic with the sort of knee jerk reaction that weak fans want. Its not a decision a football club and business the size of City should be making.