No. Gambit is not a playable character in the original Marvel: Ultimate Alliance (2006) on Xbox, Xbox 360, PS2, PS3, PSP, Wii, or PC.
The PC version has a massive modding community. Mods like Marvel Mods' "Character Packs" add Gambit, Cable, Psylocke, Magneto, and dozens more with custom powers, skins, and voice lines. Requires Marvel: Ultimate Alliance on Steam/GOG and the Marvel Mods Launcher.
On Xbox consoles, you're limited to the vanilla roster. For Gambit, play MUA2 or MUA3 (Switch).