Like the others wrote, it all depends. Caveats include:

a) Never sing anything you do not fully understand, the complete context and each single word and phrase both literally and with all relevant connotations (- native speakers often fall short of this as well!).

b) Avoid appearing condescending; ask natives prior to the event if in doubt.

c) Unless you are effectively bicultural, perfect pronunciation and imitation of the target culture is not required and may well turn against you. A foreign accent can be very charming - some even apply it in spite of better skills! The same applies to the accompaniment: best declare it "crossover".