Skirting over the complicated implications of the world "mainland" relative to Northern Ireland ... yes, and this is I believe not dissimilar to what CAF tendered for the follow-on DfT order for DMUs for TPE / Northern etc.
Looks good.
So, with the right bogie - would one of these be suitable for mainland* rail?
*mainland UK rather than mainland europe.
Pretty much yes, The C3Ks are part of the same family as the CAF bodied 332s & 333s - The only real differences being the obvious fact that the C3Ks & C4Ks are DMUs & The rather expensive Glass wrap around cab, replaced with a more normal & conventional cab front - if anything, the only changes you'd need to do to run a C3/4K over here, is to remove the wider doorsteps & fit our standard guage bogies under it.
Have to say though, whilst ill miss the good old NIR 80 Class {Rarely use the term, but they really, really are Hellfire!

} and the 455 derivative of the 450/Castle Class, Those C3Ks are absolutely fantastic replacements - Plenty of floor to ceiling height, with decent overhead luggage racks which contrary to Us mainlanders, you can actually put luggage into! The interior layout is well thought out and unlike those rancid Bombardier products, they don't seem to suffer from any underfloor engine vibrations!
There's a couple of things ill note though about that C4K - Firstly, thought Translink / NI Railways was to introduce a new livery on the refurbished C3Ks - with the aim of the C4K's carrying it too...and Notice the L Shaped light cluster - something CAF Seems to have got right first time, unlike the original 172 proposals?
Anyway, Here's an Interior phot from one of NIR's C3Ks in Great Victoria Street