Yes, returning American Army brigades to Europe would help us contain Russia:
Sustaining the ground-forces levels is the quickest way to add capacity and capability back into the force. Putting them in Europe sends Russia and others in the Middle East a strong message: We are watching you and are prepared for action.
But Carafano is preaching to the choir on this subject, since I didn't want the reduction that was carried out (see page 15).
UPDATE: Somewhat related:
New NATO secretary-general Jens Stoltenberg said on Sunday that the Western alliance could deploy its forces wherever it wants, apparently calling into question post-Cold War agreements that have been shaken by Russia's actions in Crimea and Ukraine.
I guess we finally recognized that Russian armed aggression in Europe invalidates any pledges we once made about limiting NATO troop deployments in new NATO countries. That's good to read.
Apart from that, I object to the wording that suggests Crimea is not part of Ukraine. Even if Russia abandons their efforts in eastern Ukraine, that just means they "only" succeeded in conquering Crimea from Ukraine.
UPDATE: Never mind. Stoltenberg only meant that the planned rapid reaction force doesn't violate that 1997 agreement:
NATO's plan to beef up its military presence in eastern Europe does not violate a post-Cold War deal struck with Russia on military force levels in the region, new alliance chief Jens Stoltenberg said on a visit to Poland on Monday.
I find the notion that we consider valid the 1997 agreement to ease Moscow's worries about the NATO threat to Russia when Russia has invaded a European country, threatened nuclear war if we don't accept that, and threatened new NATO states as well.