Yes, it will enhance your chances - but only within your MP status/fare paid bucket.

If you're on a W fare, for example, you'll be in front of any other 1Ks on a W or who check in behind you. But a 1K on a Y fare, for example, will get in front of you no matter when he checks in. And you'll be in front of all 1Ks on an S or T fare.

You'll be behind all UGS and in front of all 1Ps, 2Ps, and general members no matter what fare they're on or when they check in.

So it's a small benefit, but every place on the U/G list counts.