Does your basement have a French drain all around the perimeter where the floor meets the walls because you have water infiltrating issues?
If so, then you would have to have that sealed up as well if you have a radon system put in, which pretty much negates the use of the drain in the first place.
As others have said, when a radon system is installed, they seal up every single little crack and crevice in the basement. They seal up cracks in the walls. They seal up cracks in the floor. They try to seal up around your windows (if you have them in the basement). They will even put some type of cap over your sump and seal that to the floor if you have a sump. And they usually try to put the 4 inch PVC piping thru that cap in the sump for radon system.
What I find funny is that when they put the little hockey puck sized tester thing in your basement, they tell you to keep all your doors and windows shut for at least 3 days during the test. They even tell you not to go into your basement via your basement door in the house. They want everything sealed up as tight as it can be for three days.
Think about that for a second. Why would they want that? Because if you open any door or window to the basement you let fresh air in and the radon out. That will skew the test and give it a lower reading than they want to see. They want to see the highest reading they can get. But if you think about it, keeping your windows and all your doors shut tight is not what anybody ever really does for days on end. So keeping the doors and windows shut up tight is not what a real world, every day amount of radon in your basement would be based on.
Every time you go down into your basement, or open a basement window, or go out of your basement via a Bilco style door or equivalent, you let fresh air in and the radon out. You may not let all of it out, but you let out enough that if you set up one of the hockey puck testing things in your basement, and then just came and went in and out of the basement like you normally do, the radon reading will be low, and you would not need to waste upwards of $1200 or more on a system you don't really need.
Now, if on the other hand they put a testing thing your basement, and they told you to use your basement as you normally would, and to come and go as you normally would, and then they came back and said your readings were high, then I might agree with a system needing to be installed.
But under normal use of your doors and windows in your basement, a high reading is very unlikely to ever happen unless the radon where you live is in a very high concentration.
Jim