If we are able to reverse desertification, will this neutralize our use of fossil fuels?

That depends on the desert. Most deserts, such as the ones that are about 30 degrees north and south of the equator, would require massive amounts of energy to reverse or they would quickly revert to desert. In a few instances, small deserts can be change, but these are the ones created through human mismanagement. One man took over an area ruined by phosphate mining. He started by digging holes with a pick, planting trees in soil he carried in, and watering them by hand. Eventually, he corrected the problems and even had a resident hippopotamus once he had a self-sustaining ecosystem.

A desert is a desert because of lack of water. We now have some places with too much water and some with not enough. We are now 6 months without rain in Las Vegas. We mostly need higher efficiency of less waste and less burning of fossil fuels in favor of solar collectors. We need the Amazon region to stop clearing forests, and probably need to develop the underground aquifer in Africa. The issues are deep and hard to reverse.  

It will take a lot of time, and we'd need to reduce our use of fuel drastically.

The energy/carbon from the coal , oil and gas we've burned the last century was captured during many millennia