While it's extremely rare, it's not impossible. There haven't been widely publicized cases of NFL players serving in the military *before* college in recent decades. The demands and timelines of the NFL pipeline (high school, college recruitment) generally preclude such a path. Military service typically requires a significant time commitment that would interfere with the intensive training and competition necessary to reach the NFL level.
It's more likely that an NFL player might have served *after* their college career or even after a brief stint in the NFL. However, finding examples of someone serving before college and then achieving an NFL career would be exceptionally difficult.