Traditional crazy quilts made with a variety of fabrics and tons of embellishments aren't usually quilted. Traditional crazy quilts don't usually have batting either. They're foundation pieced on to muslin and after the blocks are put together a backing is added and it's tied from the back just thru the backing and muslin.
Of course that doesn't mean it can't be done any other way. I've also seen a sort of quilt as you go crazy quilt with the seams embellished with machine embroidery. I saw one that the person used an embroidery machine and did little motifs and then crazy patched them together and then quilted it in the ditch after it was put together.
I had a longarm for a while and it would be a huge pain to try and go around a lot of embellishments. It would also raise your cost in to the "custom" or even "heirloom" price range.