Firstly, can a 'single pilot certified', privately operated, N-registered, CJ2+ be flown in Europe as single crew?
Yes
Second, if same aircraft is actually operated multi-crew, can P2 log the hours and will those hours be recognised not only in the US but in the UK/Europe too?
Assuming second pilot holds a JAR licence:
a) If Captain is a JAR FI or C525 TRI, then the second pilot can log as PUT.
b) If Captain holds MCC, and second pilot holds C525 type rating and MCC, second pilot can log as P2.
if none of the above apply, then "second pilot" is a passenger.