I recently saw a video about doing this - apparently the desert is actually a really bad option if we want to combat climate change - the core problem is that the desert currently reflects a lot of light from the sun. If we cover it with forest or whatever, then suddenly we adjust the albedo of the earth and absorb more heat, negating some of the impact. Combined with the energy need to pump (and desalinate for trees - your suggestion of kelp would presumably help there) water, etc... make it not really work.
Source: https://www.youtube.com/watch?v=lfo8XHGFAIQ
I recommend watching the video - it explains it better and goes into detail - it cites its own sources.