But of course there would also have to be a discovery that profits had been underassessed in the first place. If returns had not been filed and HMRC did not have any information beyond that available when they made the determination then there would be no discovery
The information within the returns (which appear to have been completed/submitted but not processed through being out of time) could lead the Inspector to make a discovery. The legislation then dictates whether or not the Inspector can act on that discovery. The word "discovery" is interpreted as "finds out, satisfies oneself, has reason to believe".
The OP's question was "can the Revenue assess my deceased friend based on his actual returns for both years?" If the FA 2008 rules are satisfied to enable the Inspector to act on the discovery (assuming that the returns do indeed show either unassessed income or excessive relief) then yes, HMRC can assess.