It is possible, Halo CE and Halo 2 have both been ported to PC so it would seem abrupt to stop there. You will probably have to wait until they are done releasing content which could be between 6 months - 1 year.
I used to play Halo 2 and Halo 3 competitively, I even made a montage of me playing Halo 3. Good times indeed.