If you only stick to the black sea coast the first bit will definitively get you in shape. The coastal road from Eregli to Samsun is narrow, winding with lots and lots of climbing, turning, hairpins, small villages. Lovely if you're in shape, doesn't go very high either, so it won't be too cold. Some blog claims doing the whole road is more climbing then crossing the himilayas. It will likely be very wet anywhere directly on the black sea coast. But very scenic
From Samsun to the Georgia border it's easier. It's main highway East and if you don't mind doing 140km days, you could ride from cheap hotel to cheap hotel. There's not a whole lot of camping along side the road, you're sandwiched between the sea and a mountain range. Hotels are about 6 to 10 euro's a night, if you find the cheap ones. I reckon most people take the highway from Istanbul to Samsun, it's a good quality road, but you will have to climb higher then 2000m, so it will be cold.