Yes, of course.
Most shooters these days try to force strategy with a cover mechanic, or some poor campaign.
Some others try to build themselves around strategy (see: rainbow 6 (NOT VEGAS)).
Even others don't seem like they do, but they do.
Unreal tournament 2004 has strategy, and it's not "get the rocket launcher and walljump a lot."
You need to manage resources. No, it's not an RTS, but you need to know where health is, where the super-shield is, where the Udamage is, where the guns are, etc. Find optimal routes, control them. Focus on getting health, staying alive, get a tactical advantage over someone. What good is his 100 health and better dodging ability when you can have 199HP/150 shields, use a gun like the link gun's secondary (one that you're guaranteed to cause SOME damage with, if you aim remotely well), and you'll beat him with, say, 50 HP left. Now go back to your route, get that 100 HP back up, get your shields back up, etc, etc...
Just an example.