You do not need to be logged in to install Windows updates. In fact, it's probably smoother if you're not, because the Windows Update client will happily reboot the computer if no one is logged on.
Go to Control Panel | System and Security | Windows Update. In the left side of the window, click Change settings. Make sure the drop-down box under Important updates is set to Install updates automatically. This setting allows Windows to download and install updates at the specified time. If any updates require a reboot and no one is logged on, Windows will reboot the computer.
There are some advanced options for Windows Update, one of which will wake a computer if it needs updates. I have no idea if this works on a VM, but it does work for physical machines. Bring up a Run box, and type gpedit.msc. Navigate to Computer Configuration | Administrative Templates | Windows Components | Windows Update. Check out the option Enabling Windows Update Power Management... You may also be interested in Automatic Updates Detection Frequency.