You do realize if the poster's question comes true such a conflict only lasts until they get talking to locals and unless they're complete idiots they're going to figure out their limitations and like in Gate establish a beachhead around their entry point and gradually recon the area around them to insure they're secure.

Any war would be limited in scope until they know what they're up against.

The GATE series is about the Japanese dealing with this in a setting lacking high level magic barring some demi-gods and actual flying dragons nowhere near as dangerous as Smaug.

There's a sequel to that series dealing with the Navy which I'd like to see however do you really think they'd go on the war path like the Tuigan and others they aren't that stupid.

God I'd love a Stargate style series set around the GATE idea revealing all those worlds are linked and those games are the result of natives passing through Earth and telling their stories inspiring those settings unaware its loosely based on something that actually exists!