Yes, you can. Actually, anyone can use any of the WDW transportation, as long as they have park passes, even those staying off-site.
As far as how long it will take....a lot of variables. If there is a boat loading and getting ready just as you get there, it would take about 25 minutes. It is not a direct run. The boat will stop at the Swan/Dolphin first, then YC/BC, then over to BW (those two may be reversed, can't remember), then it's off to the International Gateway at Epcot.
There is a pathway from MGM that runs past BW, and takes you to Epcot. The walk is about 20 minutes. Just head out of MGM, head off to the left, with the canal on your left, all the way to the Boardwalk area. At this point go right, walk along the boardwalk, and head to Epcot. It's very easy, very well lit, and safe.