If you were a full time student, then there will be a nice gap to be accounted for, especially if you are a recent grad. If you were working full time and studying part time, then you could omit it unless the application asks all education and qualifications to be listed.
There are more drivers around with a degree, but I'm a bit undecided on how it's viewed. Certainly there is an increasing expectation for managers to have one if they want to get on, hence why a degree programmes are offered by the IRO and Glasgow Caledonian University.
Do you need a degree to do the job, of course not and the vast majority don't and are perfectly good drivers. Driving is a monotonous, often boring job and while it certainly has its challenges on occasions, its not intellectually stimulating.
I'm not sure there is a blanket answer tbh, much will depend on who is doing the interview and their attitude to the candidate and obviously the candidate's attitude to the driving role.
On a slightly different track, there is certainly some indifference and often hostility from drivers/guards to new managers who come straight from uni in shiny new suits with no job experience, let alone operating a railway and think they are Stevenson himself....