You can probably look at it with a camera that has a 90 degree mirror. But I don't think you can see too well, and estimate if the screen is clogged 30%, 90% or how much. Only that it looks bad... If it has not been replaced recently it will be covered in some black goo, with small pieces of rocks/plastic etc.
If you own the car, you do an oil pressure test and go from there, I.e., inspect the camshafts and then drop the pan if you need to. Having a camera sounds like an easy solution but you'd need it to he small, with a mirror, and lots of light (that will somehow be strong enough to illuminate oil varnished parts but not too strong to saturate the image). Think two parallel surfaces close together and you are coming in from the sides.
If your car has an oil level sensor you get more room to stick stuff into the oil pan but the pickup screen is still nowhere near easy to observe.
I guess the OP wants to know the condition of the strainer, without having any issues, just for his peace of mind.
I don't think a camera is going to provide a good enough image to get a good idea. because these cameras (even the most advanced ones I have seen) do not provide a great picture, and you need to be able to see the strainer from multiple angles.
Borescope I use at work has a great illumination and image quality, definitely sufficient to check something like what's OP wanting to do. However, it's 3/4" in diameter and the tube does not make tight bends. As said before, it would be interesting to see if someone comes up with something. The one in the link I posted seems like it could work, but spending $700 is a bit too much to satisfy my curiosity.