The LEO satellites are moving very fast, with respect to any Starlink satellite. So you will take your image and then try to find a Starlink satellite that can deal with the doppler shift of the transfer signal, not to mention the fact it is encrypted.
Nah, I’d say no. The recon satellites were not designed with a presumption that Starlink is there, and will not even have the right frequency on their imagery downlink transmitter. All the content would be classified, too, which means the entire Starlink ground team would have to be cleared.
Nice idea, but nah, no way.
Starlink has launched satellites in polar orbits. While legacy satellites may never be able to integrate with starlink, seems like new ones can be designed to natively do so. The classified content can be handled through encryption. That’s what encryption is for.
Look into Starshield.