In order to bridge an amp that way the amp must invert one of the channels on the input.
So, for that configuration (with the tweeters), one of the tweeters would have to be wired reverse polarity so that it will be in phase with the other tweeter.
As far as the choke coil, that should have very little effect on the tweeters. It acts as a simple first order LPF for the woofer.