Can a Windows 7 PC remotely manage Hyper-V on a Server 2012R2

No You cannot manage 2012 R2 from Win7 RSAT. You need Win 8.1 to manage 2012 R2.

You can use Win7 to manage 2012(non R2) (but not all function will work/show). As example in Win7 RSAT there is no "Move" option to move virtual machine. In 8/2012 - it is available. Also some VM reconfiguration via RSAT from Win7 on 2012 will fail but the same done from win8 do not fail.

I recommend using powershell to manage Hyper-V 2012R2 if You do not have yet 8.1 now.

We had same problem in our IT dept and decided to always move to latest client OS in IT Dept to be able to always manage new editions of Window Server. Before we upgraded win7 to win8 we used powershell.

ps. If You already have Win 8.1 RSAT there is a bug and You need to apply this:
http://blog.mpecsinc.ca/2009/06/hyper-v-error-access-denied-unable-to.html