EPA's Consumer's Guide to Radon Reduction says there are 'several methods a contractor can use to lower radon levels in your home', that 'EPA generally recommends methods that prevent the entry of radon', and that soil suction 'prevents radon from entering your home by drawing the radon from below the home and venting it through a pipe, or pipes, to the air above the home'. The other techniques it lists for any type of home are 'sealing, house or room pressurization, heat recovery ventilation and natural ventilation'. Nothing in the list works by drying the air.
The guide is also careful about what does not work on its own: 'EPA does not recommend the use of sealing alone to reduce radon because, by itself, sealing has not been shown to lower radon levels significantly or consistently'. A measure that is not in the list at all, such as a dehumidifier, has no such showing to point to.
Where moisture does come up in the agencies'
If you run a dehumidifier because the basement is damp, test the basement for radon as well: EPA's Citizen's Guide says nearly 1 out of every 15 homes in the U.S. is estimated to have an elevated level, and that testing is the only way to know if you and your family are at risk from radon. The reduction methods the guide lists are what bring a high result down.
What to do next: if a test reads 4