A little, but that design actually pre-dates Firefly. Could be that the person who designed Serenity was inspired a bit by it.
"I'm not big on telepaths myself. I'm not big on guns either. But if everyone else has them, I want to make sure I can get my hands on the biggest one I can."
But interestingly enough the studio model of the Baxial did actually appear in Firefly as a background ship. So I'd say the chances are high that it also served as inspiration for the Serenity.
"If you can't take a little bloody nose, maybe you ought to go back home and crawl under your bed. It's not safe out here. It's wondrous, with treasures to satiate desires both subtle and gross. But it's not for the timid." - Q
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http://memory-alpha.wikia.com/wiki/Baxial
But interestingly enough the studio model of the Baxial did actually appear in Firefly as a background ship. So I'd say the chances are high that it also served as inspiration for the Serenity.