It once was a tradition for the English upper classes to send their young sons on a "grand tour" of the Continent, which would last for many months, sometimes even a year or two.
So, yes, some billionaire paying for their kid to spend 12-18 months on a Mars trip is a possibility. Or maybe even for themselves if they retire, or as a sabbatical.
However, I think the much greater time and expense is going to make Martian tourism a much smaller market than lunar tourism.
I think in the medium term, the Moon is a much more feasible destination for humans than Mars is. It is much easier for an ultra-wealthy person to take a few weeks out of their schedule for a trip to the Moon, than months or years for a trip to Mars. Since it is only a bit over a light-second away, they could even quite feasibly work remotely from there – the delay is small enough that real-time audio and video calls are possible. Mars is 3–22 light minutes, which forces all communication to be asynchronous.