I think in a world where the major naval bombardment weapon of the 20th century can't be loaded on ships, anything is possible. Why shouldn't a bunch of stone-age farmers be able to capture and make a cruise missile work within a year?
Seriously, considering the game does expect you to believe that it takes up to 50 years to move about three miles, there've got to be a few inconsistencies. I don't think you should be able to leave a cruise missile unattended though, it's a bit sloppy. ;-)