I toured a bit in that area (Northern Hungary, Romania, Ukraine, Moldova, eastern Poland including Bieszczadzki through the Tatras and Slovenska, etc.) last fall. Roads were no worse than anywhere else, although some areas (Ukraine, Moldova) lacked paved alternates to the unpaved routes. If I'd wanted, I could've taken photos of horrifying mud and rough stone tracks....but realistically, unless you go looking for the tracks you'll do fine no matter what tires you've got. Nothing too terrible, and nothing I haven't seen elsewhere.
I was on a KLR, overloaded, with 90-10 tires (street-dirt). There were a few times I wished for TKC's, but I was glad not to be changing rear tires every 4000 miles, too. On a loaded Transalp you're not going to be getting too far into the backcountry, I'd suspect. Don't fret the tire choice unless you're either very fussy or very determined to look for mud and difficulty.
All the usual cautionary notes apply; mileages vary.