You could expect to have to do a lot of convincing to the guards on the Bath-Didcot train, I can tell you that for nothing. I'd advise you to bring all the relevant paperwork with you to back up your claim.
That would depend what route you were actually travelling.
AFAICT, a London Terminals - Didcot Parkway ticket (£22.50 CDR) would be useful for:
Waterloo - Salisbury (stations beyond Basingstoke) £34.80 CDR
Salisbury - Swindon (£27.50 CDR 'via Trowbridge')
Salisbury - Didcot Parkway (£26 CDR)
Woking - Bath Spa (£33.40 CDR route Warminster-Salisbury)
Obviously nobody would actually use it to travel to Didcot from London by that route.
You could also use it e.g. instead of a London - Bath Spa Warminster-Salisbury CDR (£37.60), £22.50 being fairly compelling compared with the £51.50 for the Any Permitted SSR London - Bath Spa or £40ish splitting at DID, but obviously you wouldn't be able to take the fast train from Paddington...
The biggest straightforward (in that it is on the fastest route) saving is Waterloo - Salisbury, and would involve probably one ticket check, on SWT - you wouldn't go near Bath....