Let's start with the actual example of the artificially generated desert that exists in the real world, called [Błędowska Desert][1]. There are some differences compared to your question but it can give you an idea what will happen since there is no change of the climate. As you can see now the dessert is slowly being grown over and that's what most likely will happen in your world's case. Since you do not change the elevation, the speed of this process most likely will be much faster since the conditions will be much more in favour of the flora restoration. So in 1 year the changes will be probably visible and in 5 year serious (for instance there'll be no longer purely-sand places), however most probably the forest will not be fully back in it's place. Also the increased amount of sand might change the type of initially dominating trees to those having more extensive roots system.

  [1]: https://en.wikipedia.org/wiki/B%C5%82%C4%99d%C3%B3w_Desert