Yeah, but the game ends immediately if they do.
The level's very possible to get through, I did it just fine first time around. I simply kept my head down, avoided getting shot and fulfilled my objective. Easy peasy.
The trick is to not consider eliminating enemies as a priority, because really, eliminating them serves no purpose unless they're directly preventing objective completion. Remember, you'll have more enemies paying attention to you, if you draw their attention in the first place.
I tend to use typically more... "subtle" methods in most games, and tend to have greater success than those who shoot first, ask questions later.
Although that does wind my team members up in FPS games when I don't just target the nearest enemy. The complain that my kill count isn't high enough, but if I weren't going for tactical strikes, their death counts would likely be a lot higher. Heh. "Use a sniper to catch a sniper!", to alliterate the old proverb....
In the immortal words of Sun Tzu:
"To gain a hundred victories in a hundred battles, is not the highest of excellence. To subvert the enemy without doing battle, is the highest of excellence."