Of course, and it is quite possible that negotiations will fail - again I say, who better than Gove - he was the one who claimed these things were going to be quite straightforward.
Thinking about this some more, there will need to be far more than just a Minister for Brexit, there will need to be a whole team.
Perhaps the smartest political move is to make this a kind of Brexit team of national unity, bringing in individuals from all the main parties. It would be hard not to agree to be involved in the most important decision in our lifetime's in the 'national interest'. Doing that would spread around the blame, make it much harder for the deal to become a party political football.
I also think it may be that the people brought in won't be those most closely involved in the referendum campaign - given the intensely polarising nature of the debate and the dishonesty then the key figures are going to be damaged goods - so no Johnson, no Gove, no Leadsom, no Farage, no Cameron, no Osborne, no Corbyn etc, etc. Also to bring in some of the more 'respected' elder statesmen might be good - those that command somewhat greater respect than the shrill whippersnappers. And including a number in the Lords so who aren't going to be worried about getting kicked out at the next election.
So here's a punt in the dark
Minister for Brexit - William Hague
Ministerial team
Michael Howard
Alan Johnson
Frank Field
Paddy Ashdown
Duncan Carswell
Alex Salmond
Caroline Lucas
Just a thought