Yes, the PPL can be done in 28 days - I did my 35 hour PPL in 1976 in 8 days, at Edinburgh, in the summer. It was extremely intensive. I doubt you will do it in 3 weeks if you cannot commit to be being at the club from dawn till dusk every day. The club will need to commit in a similar fashion - you will need an instructor committed to just you, or perhaps one other, plus of course a plane committed to you (maybe one other).
Nobody can guarantee a 4 week PPL. There may be unexpected weather etc, so if doing it abroad, consider how it will be possible to continue it later if for some reason if the training is interrupted.
