Go to the USA and have a great time - a JAA PPL IS doable in three weeks (maybe slightly more of a challenge now with the increased hours than it was 10 years ago, but still possible). Don't go if you want a holiday though - its not. Be prepared to work hard for three weeks - I was airborne at 7AM some mornings, finished flying at 7PM some days, busiest day I flew 5 hours with lesson briefings in between. But we did all the flying in two weeks, leaving the last week to tidy up on some of the exams and take it a little easier.
Some will say you can't take it all in when its intensive - believe me, you take far more in than you do if you have a one hour lesson and then can't fly again for three weeks due to the weather. One of the reasons many folk take far more hours here is the "three steps forward two steps back" syndrome. You forget things whilst you wait for a good weather day. Or some clubs/schools say "oh, you haven't done any [say] stalling for three months so you need to do some more" even though you've done that part of the sylabus. Or "oh, you need to go do some circuits because you haven't flown for four weeks because of the weather". So end up doing extra things at extra cost.
Radio is different in the US, you do need to know about US air law and airspace. But "coming back" just qualified isn't all that bad - a couple of hours dual airspace/RT/joining/etc. familiarisation in the UK should set up most people just fine.
I did the US (still going strong 10 years later), many others have. I would recommend it to anyone who could make space in their diary and have the budget to spend over a short period. No way would I learn to fly the once-a-week way.
Andy