Sure. For some reason a lot of schools suggest doing a CPL first, then an IR. So you end up doing a PPL and night rating, then hour build up to 175 hours, then do a 25 hour CPL course with around 200 hours. THEN you do a multi rating and IR course (45 hours reduced from 55 because you have a CPL) so you end up with well over 200 hours plus SIM time and it all costs a lot of money. This is great for schools for that reason - and I did just that.
However, what you end up doing is flying big VFR circles around Florida or Arizona and having loads of fun but getting very little quality training value from it. So my suggestion would be this:
If you're already paying for the plane, any extra instruction will only cost the price of the instructor, so spend 5 hours practicing and take your FAA PPL. Then fly for a while to get 50 hours cross country PIC. Make sure that every flight you do lands somewhere 50NM away. Fly at night if you can. Once you have 50 hours XC do your FAA IR - it'll only cost you the instructor rate for 20-40 hours. (In the US you need 40 hours under the hood, but only 20 of those need to be with an instructor, you can practice with a mate as safety pilot)
If you come back to the UK with an FAA PPL/IR and 170 hours, you can convert the IR in 15 hours (down from 45 hours), then do a 15 hour CPL course (down from 25 hours. If you play your cards right, you could have everything with 200 hours.
Effectively you'll be getting your EASA IR for free if you spend $2000 extra in the US.
Basically, you need to future proof yourself: think what you might need in the future and get it now while it's free. Imagine you get a job as an FO and a few years down the line you get offered command - but you can't upgrade because you only have 65 hours night and you need 100 hours night for an ATPL. You'll have to go hour building all over again. An hour in the logbook is good, but an hour IFR cross country at night is a lot more valuable.