As supervising drivers can be prosecuted for using a mobile phone - as they are not in a position to properly supervise the learner - falling asleep is a definite no no.
Since 2003, 21 people supervising learner drivers have been caught using their mobile phones
http://www.tayside.police.uk/newsarchiveitem.p hp?id=1169&mon=11&year=2007
If a learner is stopped by the police for any reason, both the learner and the supervising driver are given producers - they must both produce the relevant documents.
If the learner breaks the law the supervising driver can also be prosecuted for aiding and abetting.
Rubie v Faulkner (1940) learner committed a dangerous manoeuvre, superviser prosecuted for aid and abet by omission (failing to act)
It's old law but still relevant and referred to in court today.