Anything is possible.
The Black Forest is a similar size to Wales and crisscrossed with nice roads, but you can take in some of the best roads in a single day, and 2-3 days would get you covering a large chunk of the area with time ot stop off and poke around here and there, or stretch it beyond a week with more visiting of towns and other attractions.
I would say don't hang around there too long on the way to the Alps if you do not have a lot of time to spare as the Black Forest, nice though it is, does not compare to the Alps with regard to roads and scenery.
The B500 is the most famous road, it stretches pretty much the length of the region but when people talk about riding the B500 they mean the 25-30 mile section running from Baden Baden in a southerly direction so maybe try and squeeze that in, not far from the bottom of that is Triberg which is a pretty little town with a million clock shops and some waterfalls you can poke around (you have to pay to get in) I would suggest just stopping for Coffee or Lunch.
If you stop over for 2 nights you could put together a looping ride covering a fair proportion of the region - just look for twisty roads on the map, but with your rather short trip time I would advise just taking in what you can on your ride to the Alps