Yes it can be done, if you can't hoop it, then hoop a wash away and then pin the quilt to that in the margins. If you can adjust your speed, dial it way down. You will need to sit right by it to make sure that it's not getting hung up some where or a corner is flopping onto the design. DO NOT WALK AWAY!!!
I know that many people quilt their quilts this way, but I find it too cumbersome dealing with all that bulk. I prefer to quilt/embroider individual squares (top batting & backing), then join.