Don't worry - you get a letter from the FAA at your home address confirming that they've received your details from the CAA, and also confirming that they'll send the relevant internal FAA paperwork to your nominated FSDO (FAA local office) so that they are ready for you.
If there were any problems they should let you know then - the only thing that you need to do is ensure that you have JAA licence, medical certificate and logbook all correct and current when you travel out. If you are really worried, contact the FSDO once you get the letter from the FAA and confirm they have no issues - phone and (I think) email details for the FSDOs are in obtainable via the step by step guide I gave you earlier.
By the way, you will find it helpful to prepare for the Biennial Flight Review (which you'll need to do once you get your FAA license) whilst you are in the UK, to which end I suggest you get hold of a US chart (US "Sectional" = UK "Half Million" is what you want, although US "Terminal Chart" = UK "Quarter Mill" is also handy) before you go. You can then familiarise yourself with chart legends etc.
Even more improtant is to bone up on the regs, for which I'd recommend Jackie Spanitz "Guide to the Biennial Flight Review", which is less than a tenner and available from any random online bookseller named after a large river you might care to mention
