The radar will likely use Gold codes or another sequence with strong autocorrelation properties to reject any signals other than its own reflected beam. It generally won't be a problem.
This is incorrect. Wifi systems that don't comply with DFS show up brightly on the radar display. Here's an example from a real-world system of what a misbehaving 5 GHz AP looks like:
https://journals.ametsoc.org/view/journals/bams/97/7/full-ba...
The FCC has a list of WISP companies they've gone after for misconfiguring their wireless equipment:
https://www.fcc.gov/general/u-nii-and-tdwr-interference-enfo...