Can military aircraft send out false ADS-B tracking information?
It is certainly possible, and also happens with some regularity. Here is an article discussing a recent USAF RC-135 flight over the South China Sea in which the RC-135 changed it's Mode S identifier to that of some Malaysian-registered plane.

At some point, the plane’s Mode-S number suddenly changed, from AE01CE to 750548. That’s the ICAO number for an unknown Malaysian aircraft. The RC-135W, call sign RAINY51, then flew a racetrack pattern between Hainan Island and the Paracel Islands, an archipelago in the South China Sea that China claims, but whose ownership is in dispute.

https://ph.news.yahoo.com/u-spy-plane-impersonates-malaysian-130000120.html
Relevant twitter thread linked in the article, with ADSB Exchange screenshots
https://twitter.com/steffanwatkins/status/1303776525083381760