There is a series that covers this, but it was the JSDF and a Roman analogue and dragons and magic, but it has a pretty good idea on what would happen.
https://www.youtube.com/watch?v=qqoHn1v2JXA
about 2:45 is when the carnage really starts....
Romans vs. Modern millitary
Thanks for the heads up. I have to check that series on YouTube. The Japanese really do those type of stories well.
The Anime Network just finished episode 24 of Gate.
Episode 2 would have worked too.