I agree with John but will also add that in American English, it's perfectly normal to say "a hotel" and pronounce the "h" sound distinctly. So "a /hotel/" or "an /otel/".

No it is correct to say "welcome to THE hotel California" this how the hosts or a doorman would welcome you "to THE hotel California" I think possibly you are getting confused with when we say "an hotel" when there is no 'vowel' on front of the word 'hotel' we say '"an hotel' because of the vowel sound of the "ho" at the beginning of the word 'HOTEL'.

Also yes there is poetic licence in all art and songs that have to rhythm and match the rhythm, tempo and beat of the song. which is what the lyrics of "Welcome to the hotel California' is doing.