You can engage either autopilot BUT the (our) QRH says you are not to as there is no comparater.
If the SG fails on the side the the AP is engaged then it will drop out. But after selecting the EFU both on 1/2 switch then it can be re-engaged.
Having had it happen twice now I'm sure it is far safer to re-engage the a/p and monitor it very closely rather than hand flying the remainder of teh flight in possibly demanding WX.
From experience I can say though that often by selecting the EFI switch, giving it a minute and then switching it back to the normal position the SG normally springs back to life never to give a problem again!
SR