Yes, for example PSP core from argos = €199, PSP core from circuitcity $170+local taxes.
Are they compatible with all games/software over here?
They are compatible with all games, but not all movies, some locally purchased movies work on them (e.g. The Matrix), but some do not, so if you're after movies for a US psp it may be best to continue sourcing them in the US. You can google for compatibility lists.
Any downside of buying these accross the water?
You'll also need to get a Irish style plug for the power supply, I'm not sure of the warranty situation should it fail in the first year or two either, definitly test it over there to ensure its working and the screen is good.
If you break your PSP in any way (crack the screen, let it fall etc) and you have bought it in Ireland then if you have your receipt you can buy a brand new replacement one for e89.
If there's a fault with it you can get it replaced straight away.
This is only if you buy from certain Irish stores, check before you buy.