Will a 1" thick granite countertop span 22 inches?
The granite should span this without any problems.  But there are a lot of variables, including how thick the granite is, as well as what loads might be applied, and whether the granite is truly free of invisible cracks.

If the granite is easy and inexpensive to replace, I would "go for it".  On the other hand, if you want to play it safe, a good underlayment or some support ribs would strengthen it.  The most important thing is it needs to be evenly supported everywhere it is supported.  Just a speck on a support that prevents it from evenly seating can cause it to crack when a load it placed on it.  So it needs full contact on all supports to prevent this.

Granite is usually placed over plywood or particle board.  Many people prefer plywood, claiming it is stronger.  That is partially true, but the fact is particle board is stiffer, and makes a better underlayment.  People will argue this all day long, but I have seen it demonstrated.  MDF is puported to be stonger, but it is less stiff.  The demonstration was a simple apparatus that measured how many pounds of force are required to flex a board to a small deflection, and the particle board was the most stiff.  The particle board will eventually fail in ways plywood won't, but to support granite, the less flex the more effective the underlayment.