My old Bike is 40yrs old and technology has come on leaps and bounds since then so I'm looking for a new bike. I want to ride on roads for exercise and on tow paths and gravel paths for leisure. Will the Giant Rapid 2 cope with off-road tracks?

Assuming you are referring to the current Rapid (2), available in Canada and the UK, then yes, certainly. Depending on your tolerance for uneven surfaces, simply change out the tires for something wider/lower pressure. The bike will easily take 32s, and probably accept 35s without problem.

Have you also looked at the Giant Escape? It looks similar in concept to the Rapid, and already comes with 32mm tires on it (and might could take 35s or 37s as well).

Yes, the new Rapid 2 should accommodate 32+ mm tires. The old Rapid 2, no.