One couple
If I tried to generalise in a research study I was writing from that sample I'd be laughed out of the faculty.
There are carers as in, anybody can call themselves one; and carers as in official terminology requiring you to care for 35 hours a week minimum for a disabled person. These things are not the same. You can volunteer and study alongside being a carer (and do workfare from 2013) but you can only earn a set amount or work a limited number of hours.
If he legitimately gets DLA for the disabilty he has disclosed I would be amazed. This neither means he has disclosed all disability needs or is making a genuine claim.
It makes sense that carers can study part time (not full time sadly, I say sadly because quite a lot of FT courses are within the school day ) or volunteer as many carers will be back on the employment market one day; either because the person they are caring for dies (especially as many care for parents) or needs change or moves on in life. All the time I have cared I have done some part time study, because even 4 hours a week is better on a CV than a blank space.
My attendance even for that was abysmal, luckily I knew most of the subject matter anyhow and could get by with only the most essential lectures and making my submissions.
If I could not manage 4 hours (lots of reasons- Dh held up at work, boys kicking off or ill) I'd have made a terrible employee. If I can find suitable part time work this year I think I can now make a good one (suitable as in hours, has to be school time or around dh for childcare).
By the way, should point out that Carer's is under £60 pw; am glad I was born and paid taxes into the UK system but you'd have to be very lacking in aspirations to choose that!