Of course you'll need to lean in with it turning.
I've been sledding for a long time, and the physics between the two are pretty much the same. Biggest difference is braking, on the sled it's just the track and on the spyder it's front and rear. That would have a huge difference on "turn in" under braking.
I hang right off the side of my sled, I mean so far that my "outside" foot isn't touching the running board any more and I'm capable of taking turns at some pretty high speeds because of leaning in, the spyder will benefit from having all that weight on the inside.