So far as I know, there's no problem and you can just get on with your EASA ATPL or CPL TK training, then the flying training so long as you have the right hours.
There is one gotcha however - there are circumstances during hour building where in FAAland you'd be entitled to log the hours, and in EASAland you can't. There may be others, but the two I know are:-
(1) aeroplanes within the EASA microlight category - say a CTSW for example. These would be logged in FAAland as SEL (Single Engine Land) whilst in EASAland it would be logged as microlight and not counted as SEP (Single Engine Piston for CPL experience* or PPL currency purposes).
(2) there are circumstances where in FAAland two qualified pilots flying together can both log the time as PiC. This is prohibited in EASAland, where in single pilot aeroplanes either you're pilot + pax, or instructor + student, and apart from the very occasional case of examinee + examiner, only one person can ever log PiC at a time.
I resolve these issues (as I hold both EASA and FAA licences) by using a reasonably sophisticated electronic logbook that just adds up the numbers in two different ways and I provide different summaries in the two different regimes.
* You can count a small percentage for the CPL minima only - 10% up to a total of 10 hours I think, but you'll have to check that yourself.