How will a newer version of AGS handle an not-finished game made in an older version?
What version of AGS are you using now? If you're just moving up a few versions, say 2.5 to 2.6, you shouldn't have any problem. If you're updating from a really old version (the old DOS roomedit, for example), you may have to update your game with an in-between version first.. that's my understanding, anyway..
I got version 2.5b
You should be able to upgade without problems. Make a backup copy of your game folder first though, just in case.