Should I attempt to repair a leak in my radon mitigation system's pipework?
Since it's low-volume and outside I wouldn't worry about it, but Ed's right that there's some indication of blockage. There should be very little back-pressure on that pipe.

However, I've never seen downspout used for radon systems. I'm not sure how you'd reliably seal that (and it may not be legal where mitigation is required by code). My guess is that it was never completely airtight. I'd be replacing it all with welded PVC or ABS and replacing that mangled no-hub coupler.