So I just completed Mass Fusion, and I'm wondering what will happen if I go to the Prydwin right now and kill Maxon for his sweet looking battlecoat? Will Airship Down be different in some way, when I do it? Will I still even need to bring down the airship with their leader dead?

I believe once you begin airship down, you become an enemy to the brotherhood, therefor you can kill him and take his coat from that event, and his Elder Power armor, which is top level T-60 power armor with an elder emblem on the left arm.

I became an enemy to the BOS once I did Mass Fusion for the Institute.

So if I attack him right now on the Prydwin all I'm missing out on is his Power Armor?

You still get to blow it up don't worry, I killed that guy when I heard his Hitler speech, you won't screw up the ending from it.
"We won't rest until the Synth threat is wiped clean from the common wealth"
BOOM headshot