ccoffin,
I cannot help you with a direct answer to your question as we don't tow a suburban. We tow an '11 GMC Sierra 1500 4x4 Extended Cab and, carry a Honda GL1800 Goldwing in the back of it using a "Rampage" lift.
Now, according to my 2003 Dinghy Towing Guide, your Suburban 4x4 IS flat towable and, according to the "notes" that are with that particular vehicle:
** Transfer case must be in NEUTRAL, ignition in the OFF position, and the fuse removed.
We don't have to pull any fuses for our GMC so, like what's been stated, you should dive into the owners manual for it and see what it says about flat towing behind a motor home etc. Now, one more thing. It also states your Suburban is in the vicinity of 5123 lbs. Well, you can take that for what its worth or, do like I've done and take your Suburban to a certified scale (Refuse disposal, Recycle establishment, Moving and Van business etc.) and REALLY see what it actually weighs. I've proved those Dinghy Towing guides wrong twice in a row with our toads.
Our GMC is supposed to weigh 4875 and is sitting right at 5300 with a full tank of fuel. So, the reason I push this is, if you've determined the weight of your coach, the GCWR of it, and calculated what hitch/tow bar system you either have or are thinking about purchasing, your ACTUAL weight of the Suburban may put you over any given limit. It's always good to be dead sure of what you've got. Good luck.
Scott