I visited Croatia in June of 2001. Had a beautiful trip on the coast from Split to Cavtat (south of Dubrovnik) and back up to Zadar, then on the inside for just a few days. Generally travelled by boat from island to island.
I have seen very little of the road, but it certainly didn't look like 700X23C tire-friendly to me. Plus, as far as I remember again: no shoulders, and fast drivers. And LOTS of hills (which is cool with me now). I could totally see myself cruising around on a big bike, but not doing a long distance trip. However I have heard of a few people who did, but no one that I know personally. I would google that for sure and, if dealing with a tour operator, ask to talk with past customers who did the trip.
Regarding Croatia: I had a wonderful trip, and it was certainly made better by the fact that I had taken the first 30 lessons of a "Teach Yourself Croatian" kit before I left. Sure, English and a bit of German will get you to most places, but really not that far. It's not very hard to learn (unlike Serb, which uses the Cyrillic alphabet, Croatian uses the Latin alphabet, same as English) a few words, and it will make a HUGE difference in your enjoyment of the smallest experiences.
Italy is probably more bike-friendly. But SO much more expensive, and more familiar too. And the pasta and espresso are just as good in Croatia. (Stick to white wine though!)