Can I cycle to Frankfurt Hahn airport from Koblenz?

Yes, that should be absolutely possible and a pretty nice route. There are bicycle paths along the river, and you should leave the river shortly after Zell and go along the Altlayer Bach towards Altlay.

Interestingly, according to Google Maps, there is a shorter alternative route that continues down the Rhine, leaves it at Bad Salzig and includes a long stretch of the Schinderhannes-Radweg.

There is also a good website for routeplaning on bicycles, which will help you. You can even see the gradients of the road and have different options (only bicycle paths, the fastest path, the shortest path ...). I tried it myself and find it more accurate most times than google maps for bicycles.

RadroutenPlaner

My suggestion would be: take only bicycle routes and try to avoid gradients. The RadroutenPlaner would suggest a route of 86,8km, having a gradient of 849m and (by traveling with 15km/h) you would need 5:47h.

If you have a GPS, you can even download the route you calculated.

Important Notice Don't try to navigate to "Frankfurt Airport" ... didn't know that either, but Frankfurt has a district called "Flughafen" (which means airport), so it will navigate you in the wrong direction ;) Try Flughafen Frankfurt-Hahn