How could a stronger bumper cause an airbag to not deploy? If anything, a stronger bumper would transmit a STRONGER crash pulse to the sensor, making it MORE likely to fire. The problem would be that it would fire in milder impacts than usual, perhaps in something like a fender-bender (as an example, but I doubt it) which would result in a much more expensive repair.
Yes, it might cause the airbags to fire a bit sooner than they normally would as well, there's a chance the airbag might not still be "fully" inflated by the time you come in contact with it, but I doubt this is really an issue.

Brent