You should be fine with doing the above. A few of the US schools advertise that fact they'll get you through the rest of your PPL if your having trouble finding time/weather to fly in the UK.
if guys can complete the whole ppl in a month surely half of it will take 2 weeks?
Be aware of threads about people not completing their PPL in 4 weeks ay the US schools. Their 21 day PPL course more often than not takes longer than 21 days.
I'm not sure how long 20/25 hours would take with OBA, but I think 2 weeks should give enough time to get it completed?
You'll need to get used to a new school / management / AC's / FI's.