A beer connoisseur I am not, but I do know a good milkshake when I find one.
I just spent some time Googling to see if making milkshakes with Abita's Turbodog brew is common practice, and while I didn't find many references to actually mixing it with ice cream, several sources—including the Abita website—suggest that the dark brown ale has distinct chocolate/vanilla/toffee flavors that I suppose make it a natural pairing in the house specialty milkshake ($5) at Po' Boys & Pickles in Portland, Maine.
As the name suggests, this place is a Big Easy tribute plopped down on the outskirts of downtown Portland. No surprise, then, that they're pulling pints of Abita, but you'd never guess that this shake is chocolate-free. It's just Turbodog and vanilla ice cream, and whipping the two together somehow makes for a distinctly chocolaty result. Not sweet chocolaty, though; just rich and malty, deep and lightly bitter with a good boozy finish. There's also a bit of carbonation in there, which keeps things light and fizzy under that blanket of whipped cream.