Under normal conditions, no problem. The road is packed gravel and sees all sorts of bikes and motorhomes.
I ran into a Can-Am Spyder on it a couple of years back and he had no problems with clearance, handling, etc. so I would expect your trike should be fine.
In regards to the HD, it'll get muddy but just make sure that he is comfortable handling a big cruiser on gravel roads before hand.
To compare to your local roads it's better than Chute Lake Road and roughly about the same quality as Brenda Mines Road, although with less loose gravel.