>If anyone wants to come, they IS welcome????? I think not.

no, of course not. editing to obviate the issue you'd get:

everyone who wants to come is welcome
or
all who want to come are welcome

what's confusing, to someone trying to logically parse the language, is why anyone would want to write:
if anyone wants to come, they are welcome. [antecedants be damned!]

and, to think that we are excluding someone by saying "if anyone wants to come, he is welcome" makes the whole thing illogical.