As ETech7 said, yes, you can access that drive from the other computers across the network. The only catch is that you would have to leave the Windows 7 computer on in order to see the drive.
Now if your router has a USB port that you could connect the external HDD to, then you might be able to save files to it regardless of if the Windows 7 machine is on or off.
Now if your router has a USB port that you could connect the external HDD to, then you might be able to save files to it regardless of if the Windows 7 machine is on or off.