Sure, happens all the time. Synthetic aperture radar satellites operate in different bands than air traffic control radar, so there is no risk. Your house is scanned at least once every few days from wide swath radar satellites like Sentinel-1.
Sounds like some disaster response, some scientific, and some commercial uses.
I think there are other non-ESA European (and national) agencies that work on military use of space. For example, there's apparently an "EU Satellite Centre" based in Spain that is concerned with military use of space (and is not part of ESA).
https://en.wikipedia.org/wiki/European_Union_Satellite_Centr...
I do imagine that military users can probably buy or access data from ESA sources on the same terms as civilian users and that they probably do so.
https://en.wikipedia.org/wiki/2012_National_Reconnaissance_O...