Unless you are looking at a truck under warranty, I say avoid the dealer at any cost. The simple fact of the matter is even when HUMMER was in its heyday the number of COMPETENT H1 techs across the country were not that high.
Here's the simple and honest truth: You are talking about buying a truck that hasn't been made in four years, the number of HUMMER dealers that even have an H1 tech on staff today is virtually non existent (barring a few). Hell, there are hardly any stand alone HUMMER dealers left!
The engine is a standard GM 6.5 G series engine (found in GM vans)
The trans is a 4L80-E (found in heavy duty trucks of that era)
The transfer case is a standard NP242 and is not harder to service or rebuild that any other chain driven transfer case
The diffs are AMC 20 variants they are a little unique, but nothing a competent tech cant service, and there are a couple of great guys to get remans from should you ever need a new one. Same goes for the brakes, half shafts, yeah its different... So what its simple.
The geared hubs are unique and most people won't want to touch them. If you have a bearing failure of something that warrants opening it up there are a few highly recommended people throughout the US for you to send them too for rebuilding.
The HVAC system is largely based of a GM, any HVAC shop can work on it.
CTIS, that one scares everyone. I'll tell you a little secret though.... It is VERY easy to fix when there is a problem.
See what I'm getting at here? The truck is a mutt as far as parts go, alot of which are GM (never mind the steering column that came out a a ford escort), most of which are not that special, or any harder to work on than any other truck. The long short of it is yes your GM dealer should be able to service your truck. Ask them if they have a Hunter alignment rack, if they do they should absolutely be able align your truck. Tire balancing can be harder to find, most shops cant balance a 37 + inch tire, a local 4x4 shop should be able to help you out there.
Buy the beast, if you are happy with your local GM dealer take it there for service, and buy your HUMMER specific parts/accessories from
www.rubberduck4x4.com. Travis @ RD4x4 is a standup guy to buy from, he'll find you what you need for the most fair price out there, and he's a fun guy to talk with. Good luck 911, where are you located anyways.