While one solution might be to setup reverse tethering, as eldarerathis already pointed out in his comment to the question (see: How to set up reverse tethering over USB?), this most likely requires your device to be rooted.
An alternative approach is described in an Article I've recently stumbled upon: How to extract direct APK links from Google Play Store. This basically uses a Java app on your PC, which is connected to your device via USB cable – and hence would perfectly match your needs.
You would need to download that Java application (Real APK Leecher), install it on your PC, configure it with your device ID (which you can find e.g. via the "dial code"
*#*#8255#*#*), and then this Java app pretends to be your Android device, so you can use it to browse the PlayStore and download apps to your device.
Disclaimer: I didn't try this for myself, so I'm just sharing my find with you here.