If it was a private buy for £5k> then an AA check is wise.
But its only £1k, and its from a dealer so you have some comeback if it turns out to be a lemon anyway.
So no, not worth it.
Edit: If you have the logbook details you can view the MOT history online, and see all the failures and advisories.
When we got our car the new MOT it had contained no advisories, but the car had a list of faults, some that I fixed, a couple that the seller fixed when I returned it.
Afterwards, I found the MOT history site, enter the latest MOT cert details, and all the previous MOT’s had advisories as long as your arm, and the car still showed them all despite the latest being dodgy. If I’d noticed sooner I’d have reported the garage for a below standard MOT. The rear shocks had no damping effort whatsoever and there was a seriously under-inflated tyre for starters.