Is she registered with the BGS? If not, then it is also much more likely that she is not CAE tested.
The chances that she is infected with CAE is fairly low. Only very few goatbreeders in the UK are scrapie-monitored (it is an export requirement, but not much else needs it). I would say also only a small % of UK goat herds (non-commercial) are annually CAE tested or are CAE monitored. It is an extra cost that most of us find hard to justify, but it is a requirement for showing your goats.
It is difficult to advise without seeing the goat and speaking too the present owner, but as I do show my goats I do an annual whole-herd test (just got my certificate and now dreading the bill at the beginning of March)
If you do take her (and her female kids???) you would then have to decide if you need that assurance for your herd for the future. If you were planning to show or on using a registered pedigree billy on any of your goats you will have to do an annual CAE test. Most of the pedigree breeders will not allow the mating of non-CAE tested females to our males. It is a simple bloodtest, and as long as you could bring your animals to the vets (rather than have a call-out) to take the samples the cost is not too onerous for a couple of goats. Unless you plan on bringing in outside stock regularly you could probably rely on initial test and then only test the goats that you are planning on breeding that year.
I am a bit more worried that you are saying she is quite thin. However if she is feeding twins she will need quite a bit of concentrate to produce enough milk for them - so if she is alert, bright-eyed (and bushy tailed) she should be fine. Also have a look at her feet (are the horns overgrown to make her look like wearing slippers?) If yes I would be a bit worried about the general care she is receiving at her current place and why the current owner is so keen to let her go, how does the current holding fell when you were there? Goats inquisitive and coming to say hello to you?
The uneven udder may simply be that the kids are feeding both from the same side - you would have to watch this and strip the milk out once a day from the "underused" side.