I'm using the "Desktops" program by sysinternals. I'm wondering if it's possible to move a screen to one of the other virtual desktops?
No it's not. From its webpage at http://technet.microsoft.com/en-us/sysinternals/cc817881.aspx.
Desktops reliance on Windows desktop objects means that it cannot provide some of the functionality of other virtual desktop utilities, however. For example, Windows doesn't provide a way to move a window from one desktop object to another.
You can use other virtual desktop programs though.