i was just going to say 'yes' right off the bat, as i had raised my polar bear rug before... but now wondering if thats how i did it.
the bear has to be 1 click above the floor stuff, or it'll flip. sometimes only bits of it flip (and there are a LOT of parts to a bear rug!)... at 1 click, you can still walk over it.
let me double check and get back.
edit
yup, works fine with gozas.
3x3 squares of goza.
raise them all 3 times.
place bear rug.
RAISE one large piece of bear rug (i used the butt end)
LOWER the rest of the bear to the floor.
Raise the floor bits up 2 clicks each, until all pieces line up, except the one piece you raised higher.
this is just to make sure you have the bear at correct hight, not to get flipped with floor detail, but low enough to walk on. axe the goza's as you go. once the bear is broken, they aren't really needed, so long as you don't accedently connect your bear rug up again.
once you're sure of your bear rug placement, lower the highest piece to match up with the rest of the rug.
he's now whole again, and can be axed and redeeded if needed.