There's quite a bit to unpack, here.

When - as in time of the year - are you planning on doing this visit?
How long have you got?
Where in Sicily are you planning to go?
As KLouis is saying, are you planning on stopping by in Matera as well?

If you have 2-3 weeks, by all means do it. If, on the other hand, you have something like 7 days, in the dog days of summer, and you want to go from Napoli to Ragusa and back via Matera... May I suggest a trip to the dentist instead? It'll be quicker and possibly less expensive.

A "simple" journey from Napoli to Taormina and back via Matera is 1,234 km (plus the ferry). If you're planning to go to Palermo, for instance, it's 1580km. The driving time alone will be about 12-17 hours, non-stop. And in the summer the A2 does get busy.