Ah yes, I can see where there could be a problem using the VM module to login, as it is restricting code for the Module since they are not logged in yet!
The quick solution and answer is yes, you can use the Joomla user login (either mod or component) to have VM store users login. It's one in the same. The difference is registration, to which we have solved.
If you still want to show the VM module once users are logged in (using Joomla login mod) you can set the VM mod to show to only REGISTERED users. This way the mod only shows once users have logged in through the J! login mod.
The problem with this is, you might now have 2 "Users" modules showing when a user is logged in, and frankly, you might not want to show the Joolma login/out module once they have logged in. You can use METAMOD (a free module, search the JED) to disable any modules once a user IS LOGGED IN.
In other words, this cool mod does something Joomla doesn't inherently do. Joomla only allows you to disable mods to UNREGISTERED. This mod will allow you to disable mods to REGISTERED users.
I have used this many times to change out the main menu of a website depending on whether they are a registered or non-registered user.
Best.