Searching for Dyson spheres is not too different from searching for other hypothetical astronomical objects. Maybe it is a low-stakes analysis you could put some students on, so they learn something. Data collection, statistical methods, paper writing is all identical to "traditional" searches. I come from particle physics, and we did quite a few searches for very weird particles that, I admit, didn't believe in. But it was quick to retool the search for more plausible models.

Also I think science works the way that you use your fantasy to come up with outlandish things, and then try to rule them out with logic.