No, you can strip it off really easily. That's how I picked up all my fabric screens so cheap - the lady who owned them didn't know she could strip them, so once she was done with her shirt run she sold them for $20 each!
The one thing to note though is that the stripping chemical is often tied to the emulsion you use to set the image - different brands don't usually work with each other*. In cbr, you can coat a screen at Megalo for $5, and strip it for $2 (there are other fees too - hire, etc). If you're doing it at home the stripper I use comes as a powder that makes up a huge amount of liquid when mixed. I don't know how much it would be per screen but it would be $1 or less.
I usually do a few pedals at once, so I can get three or four stencils on the one screen, print them all and then strip it.
*Having said that, there is an ultra-caustic process that will strip anything, so if you find a good second hand screen but don't know what they used to put the image on it is still possible to get it off, it's just gross.