Yes , if you mean capable of going affiliated at any level.
She will need to look for unbacked or older horse looking for easier life for that money.
Her only other option is to look at a good New Forest, Connemarer(sp) or Welsh Pony as many are capable of doing Dressage at a serious level, but I suspect even then she will strugle for 3k.
I think very possible to find one maybe just backed that shows decent enough paces and flair. I certainly don't think she'd find a 'ready-made' one for that amount though! I have seen a nice animal on HM they want £3K for but that is 3yo unbroken (as yet) to make around 16h. They want £3k for that but personally I think is a tad over-priced (because it's coloured). I think it'd have potential to do most things though - an unbroken 3/4yo is a pretty blank canvas really isn't it so provided it's conformation and movement is good enough that'd be enough to work from surely?