Maybe the fares experts will know.
I expect there may be some in the mornings, since most off-peak tickets have at least some morning peak restrictions. That said, for any given train departing a given station in the morning, in order to rule out the possible existence of an off-peak ticket valid on that train, the number of possible off-peak tickets that would be valid on the relevant route and TOC, for which you'd have to check the restriction code, would be enormous.
In practice, railway staff need only check the restriction code on tickets actually presented to them for travel on a given train, so they don't have to attempt to answer the question you're asking.
I don't know why, but some of them do seem to ask themselves that question, imagine they know the answer and then confidently proclaim "off-peak tickets are not valid on this service". And then we keep coming across examples of off-peak tickets that are valid on that service.
It is often said the reason for this is because the vast majority of passengers holding off-peak tickets won't be able to travel on the train in question and it is important to warn them. The obvious solution would be for guards and train managers to announce something like:
"Off-peak tickets with restriction codes [quote the restriction codes they see most often, are familiar with and are sure aren't valid on the departure in question] are not valid on this service. If you hold an off-peak ticket, please check the restriction code to see if you can travel on this service. [Repeat first sentence]"
The vast majority of passengers would see that their ticket had one of the restriction codes quoted in the announcement and would know it wasn't valid on that train. Anyone with an unusual restriction code could check their itinerary and/or the restriction code to establish if they were valid or not. Nobody would be misled or wrongly denied travel. Alternatively staff could just say nothing and then go round collecting any excess fares that may be due (after checking any unfamiliar restriction codes to establish validity or otherwise, of course).
