I have a bad rear differential (one of the driveshaft seals is shot, and almost all the oil is gone), and I was wondering if this can affect my automatic ZF-6HP26 transmission.
As Moab states in the comments, a bad rear differential cannot hurt an automatic transmission. The only thing attaching them is a driveshaft. Other than that, they are completely independent assemblies.
Even if you've already done irreparable damage to the rear end, you can most likely prolong its life by topping off the gear oil and fixing the seal. Even if it is noisy, you might find getting these two things done will quiet it down and keep it going until you can plan on fixing it, either through a rebuild or replacement (if it's needed at all).