I am about to try to be the maintainer of a program, but I have yet to try to use wine successfully. If I download a program should I only be given the option of using the Ubuntu Archive Manager or should Wine be an option in the dropdown menu.

That's a question to your distro forum. To run wine you do:

I was not asking how to run it. I was asking if Wine acts as the installer of the program of if it is just used to run the program.

It can do both. use Winetricks to install programs.

Wine runs Windows software... if the software your running is a setup.exe or install.exe (or .msi) that installs software, then Wine runs it just as it would anything else. After you run the installer in Wine, you then run the program it installed. Wine doesn't tell the difference in running software and installing software, an installer is still just running software.

Thanks.