Can a user share their screen with me without any interaction from user?

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I work in an organization and I have a free program on all our machines called **bleep**. A user can send a code and then I can remotely access and control their machine.

When I purchased TeamViewer, I was under the impression that I would be able to install the TeamViewer MSI and it would allow me to access a users screen without any Interaction from the user. When I am logged into a computer and then I attempt to connect to that computer from another computer, instead of seeing the users screen, I am gretting with the option to log into that computer. If, on the computer with TeamViewer installed, I send a code, then I can share the desktop with the user.

I already have a free program that does the same thing, the purpose of buying TeamViewer was that I wouldn't have to ask users to share a code with me everytime I wanted to access their machine, similar to how another TightVNC works. Does TeamViewer allow me to access another computer and view a users screen without any interaction from the user?