Yes and no. Can you drive from Halifax to Cape Breton, do the Cabot Trail, and come back the same day? Yes. If you leave at 4 am.
Would it be a waste? Yes.
Stay in Sidney? By god no.

Do yourself a favour and add more time for Cape Breton. It is gorgeous. But don't waste time on Sidney or Sidney Mines. Stay somewhee ON the Cabot Trail. Or in Bay St. Lawrence (North of the Trail). Or on Isle Madame. Or in St. Peters. All of those are much nicer than Sidney.

Dingwall Beach is great during sunset.
The next evening, watch a sunset from around here https://goo.gl/maps/u4aW1CRcifLHivPz6

In the unlikely case you take an interest in aviation, you want to visit the Alexander Graham Bell museum in Baddeck.