Sorry, that's not correct. If you and your bike weigh 200 lbs and you have your tires inflated to 100 PSI, then you wlll have a total patch size touching the road of 2 inches. Regardless of whether or not you have 23mm or 35 mm tires.*

Wider tires wear longer for two reasons:

1) for a given pressure, they deform less. This is why wider tires have lower rolling resistance.

2) Consider the angle the contact patch makes with the wheel. It is a small angle in all cases, but for a narrow tire, you have a narrow but (relatively) bigger angle where as on the wide tire, you have a wide, but smaller angle.

Cheers,
Charles

* You might notice that as your tire pressure goes to 0, your contact patch does not become infinitely large. So this formula only works when the tire is inflated "reasonably."