There is a HUGE list of potential problems that an '85 GL1200 could have, and my '85 LTD had most of them. But it had also been badly abused and neglected. It sounds like yours has been neglected anyway, but that does not mean it will have all the problems. I would do the belts, just to prevent the engine from destroying itself. Not much point in getting it running good, just to have it blow up.
If the carbs were never drained, after 3 years you are definitely looking at a complete carb teardown and clean. I'm not familiar with GW carbs, since my LTD is fuel injected. So get a manual. And do one carb at a time, don't mix up parts. replace any gaskets and hoses/vacuum lines as necessary, make sure there are no vacuum leaks. Make sure your fuel filter is clean, and the lines are not restricted. With the gas tank almost empty, you can see inside it pretty good through the filler opening with a 2 AA Maglight. Mine only had one small round spot of rust right below the fuel filler. It looked like surface rust, so I left it alone.
There is a lot of other maintenance that should be done on a bike that old, the kind that almost nobody ever does. But it is better to get it running good first before getting into the rest of it.