Running the two softwares on two different screens isn't usually an issue, not is adding the programs to the start menu to have them start on bootup. The issue I see is the window focus. if the person is using a writing pad to sign there name and I presume you want them to see if on the 2nd screen, when they sign, it might shift focus to that application, it might not. If you are in the POS software and just made their bill and waiting for them to sign, will the signature software recongize the input and display right away.
Only real way to tell is to try both at once if you already have them, just make the windows small and see what happens. If it works fine on 1 monitor, it shouldn't be a problem with multi-monitors. It's just a matter of how the applications work that isn't under your control.