Seems like every question here gets answered with "It depends." This one's no exception.
Technically, your 2x3 Speed is a medium format camera, shooting negatives that are 6x9 cm. Large format begins with the 4x5 size, and moves up through 5x7 and 8x10 (and bigger, but that's getting into rarefied stratosphere).
The answer to your question depends on what you mean by "large format." Both sizes of Speed Graphics are basically handheld cameras with big negatives, so if "large format" means the kind of stuff you get with a monorail view camera, the Graphics can't do it, though the 4x5 has limited rise and tilt, and the 2x3 a limited amount of rise. But if it just means getting that bigger negative, and the clarity that comes with it, you'll do all right.
Many's the photo student of the 1940s and 50s whose first experience was with a Graphic. The longer lenses (101 to 105 on the 2x3) are a little less forgiving in matters of focus, make sure the rangefinder is adjusted for accuracy or things will look fuzzy!
I agree that the rollback is the way to go. If your 2x3 is from the 50s, it should have the Graflok back, which you'll need for the back (the Graphic "23").
All in all, the Graphics are fun to use and designed to mesh well with your intuition. Have a tech go over it before taking it out for a spin, though. Good luck!