They are not allowed to post a fare online or in print without the fuel surcharge in it, but they most certainly can charge one.

If for example your ticket cost $700 plus government fees and taxes (making up numbers here) according to the Department of Transportation, they have to show a price inclusive of all fees except airport and government related fees and taxes.

They would have to show a fare of $700

They could not show a fare of $373.80 and than say plus fuel surcharge of $326.20 in tiny print. They have to show the $700, and if they feel the need to break it down into base fare and fuel they can do that in the tiny print.

So they can have one, but it has to be included in the fare in their print and internet advertising.