Can a U.S. citizen marry and legalize an illegal alien without the immigrant going back to his country

The answer to this question would depend on several factors. One important factor would be what you mean by "illegal alien." If you mean that the person entered the U.S. without a valid visa then his opportunities to adjust status will be severely limited. If however you mean that the person entered the U.S. on valid visa status and then overstayed the visa then this is a different situation.

What is certain however is that merely marrying a U.S. Citizen does not automatically make a person a legal resident of the U.S. It is therefore advisable to seek specific legal advice from an immigration attorney as the detailed facts of your case are extremely important.