I know of at least a couple of RVs in Portugal.
I have flown in to Alvor on the Algarve, which is a quite busy GA airfield. Quite a bit of air sport activity nearby at Lagos. No real problems with GA touring and Avgas availability.
Operating a N registered experimental may be allowed on a short term exemption, but you would need an exemption for each other country that you want to fly in. Long term it would be better to register and get approval locally. Reciprocal agreements allow relatively free travel for European homebuilts although Portugal and Spain are more bureaucratic requiring separate exemptions for each visit by a foreign homebuilt.
All this based on knowledge from experience about 15 years ago.