Yes, with caveats. I bought the game for the 360 on 11/11/11. Played through into January - several false starts and 1 major Orc fighter character called Rhas AlGhul. I then switched to playing ME2, then ME3 when it released ...

After that ...situation... I started playing Skyrim on the 360 again, with several new false start characters. Finally got tired of waiting for the latest patch for 360 when the PC 1.5 patch was already out, so I traded in the 360 version and bought the PC version. Boy was I missing out playing the 360 version (love, love, love the mods - USKP, UFO, CBBE, URWL, etc). Still had a couple of false start characters, but finally found 1 I like so far (Drusilla Darkbourne - pure mage but has just discovered she's a vampire - Vampire Overhaul mod). Haven't stopped since switching to PC version.