Do it. I have done POE over 4 pair untwisted pair stranded 24awg up to around 60-70 feet. I also have a Doorbird working flawlessly on POE over the same wire at close to the same distance. No issues with video or control.

You could always run something like iperf to test throughput. There are products out there that will send ethernet over 2 conductors of virtually any wire type you can imagine. Mobotix 2wire is one we have used a handful of times with no issues. There are others as well. But I would go ahead and use what you have first and just disclaim a plan B option to your client. :)