YES Network in the past occasionally showed an A or AA game, but it's been so long I can't recall if they are in HD. I don't think they have done any minor league games (yet) this season. (If any at all)
I read recently somewhere (I don't remember where) that since the Yankees moved their AAA to Scranton/Wilkes-Barre they have not shown a AAA game. (Don't remember if they did when they were in Columbus)
It's too bad the MLB Network doesn't show any.
Looks like today's game Williamsport Crosscutters at Brooklyn Cyclones is in HD on SNY, the Toledo Mud Hens at Buffalo Bisons on 7/19 and the Staten Island Yankees at Brooklyn Cyclones game on 7/23 (replay 7/24) (also SNYHD)
At least the Mets are putting the games on for their fans. Yankee fans are left in the dark.