not being funny, but why dont you just bring the HDD with you into work, what you suggest above is remote access to your PC which can be done, but the router is nothing to do with it, but still dont make sense why you would want to remotely connect to a USB HDD when you can bring it with you.

then it wont work, you need the host PC to be on to access the drive

or use a flash drive instead of usb hd.

I dont want the pc to be on. I just dont want to carry it around a USB dont compare to a 320gb hdd. Just wanted to now if it was possible