Not really. May created a Brexit ministry and appointed leavers to all the key positions. Labour appointed remainers to shadow them. It wasn't May's fault that she was elected leader.
As was very clearly shown in the election, there are a great many Labour voters who defected to UKIP in 2015 (and went on to vote leave). That they then came back to Labour was a much better reason why they did better in the election than the youth vote. For this reason I firmly believe that...
The referendum wasn't fought on party lines, there were people from across the spectrum on both sides. I would definitely support a cross party negotiating team with one proviso - they must have supported Brexit in the referendum. That would rule out Starmer and most of Labour's front bench.