Can the signature of stealth fighters be uncovered, and then used for future detections?
I would like to make some general comments, as having worked on programs stood up to build sensors for various military threats. In these programs we were always attempting to get data on relevant threats. The more challenging the signature the more it drove the sensor technology, hinting at areas of improvement. In the sensor research we often met with the target community. At times we used their services to look at sensor sensitivities. Perhaps not surprisingly, even though they were on our side, they were at times reluctant to talk about certain sensitive areas.

What I learned from this experience is that, if you are the target you hide your signature as much as possible, and if you are the sensor you hide its characteristics as much as possible. Whenever you give away information you risk exposing your vulnerabilities, and each has its vulnerabilities. An example might be controlling creation of photographic images of sensor optics on an air-to-air missile. This is why some "black" programs hold their technology in war reserve (think hidden in hangers), and are only utilized when the threat warrants exposing this new hardware to the adversary.

As another example, I can point out missions during my cruises aboard the USS Nimitz flying light attack. During this time period the battle group often passed by Libya. The carrier stayed out of the contested waters while the destroyers breached the line drawn in the sand by Gaddafi. Other missions included flying electronic surveillance platforms with fighter escorts close aboard the coast. The radars would light up the surveillance aircraft and that data was captured for further analysis.

My assessment would be that, whenever you bring out a new technology you try to cloak it as much as possible. The other side is out there collecting data on you. Sensors improve, and targets find better ways of hiding. A good example of the evolution of threat can be found looking through the literature on surface-to-air missiles. As soon as the Russians came out with a new SAM we came out with a new countermeasure, which drove them to better sensor technologies. 

The findings that a collection activity might obtain will more than likely not allow them to "easily" spot the target. This sort of technology is on the "bleeding edge" and gains are typically hard won and incremental. As we get better sensors, they get better at masking their targets. 

One last observation which might not be obvious, but definitely quite important, is that the target might use information about the sensor to develop tactical procedures to minimize its effectiveness. If I learn that your sensor is using microwave electromagnetic radiation I will think about hiding in water vapor or rain storms to minimize its effectiveness. It is truly a cat and mouse game.