I'm developing a Windows Phone 8.1 app in Visual Studio 2013 Pro on a Windows 7 machine. Obviously, using the emulator is not an option for running it.
Is it possible to deploy/build a Windows Phone 8.1 application to a device (an actual Windows Phone connected via USB) on Windows 7? (I'd find out myself, but I don't have a Windows Phone. My client is willing to purchase one if that will enable us to run it.)
Sure, but you should have developer unlocked device to deploy your application. To unlock your device, you can use Windows Phone Developer Registration tool coming with SDK.