Does a full professorship necessarily imply tenure in American Universities?
It depends on the institution whether it is even possible, in principle, to have nontenured full professors.  At some institutions, being a full professor automatically means you have tenure.  At other places, it is merely overwhelmingly likely that a full professor will have tenure.

Any case where somebody is a full professor but does not have tenure is likely to be a bit odd.  In my department, there have been, in the last twenty years, two people who had the title of "professor" without being tenured.  One of them was a senior person who the department hired, but for some reason they could not hire this person directly with tenure.  Instead, they were hired as an untenured full professor, with a two year tenure clock.  They turned in their tenure file after one year and got tenure with no problem.  The other person is a former tenured full professor (and department head), who moved to an entirely soft money position.  He was allowed to keep the title "professor," but he is no longer tenured, with his position coming up for review every three years.