"Not to mention a confession from Brooks, who says he'll plea-bargain,
but only if he talks to you and Captain America here."
Captain Frank Irving
Usually when there is a pop culture reference with no allusions to its source (which I love!), I take the position that it's based on reality.
But I think in this case, I'm going to go with it being a reference to the comic book character.
First off, this show doesn't take place in Earth Prime-Time, in which not only is the character from the original story real and adherent to that plot-line, but characters in other TV shows are familiar with the Washington Irving story. (See the 'Murder, She Wrote' episode "Night Of The Headless Horseman".) And as with many "true" stories in the main Toobworld, it is regarded as fiction by the general public.
In the main Toobworld, Captain America, like Ichabod Crane, is a real person. Known by the public as Steve Rogers, he was briefly seen in the late 1970's (played by Reb Brown). He may still be in service for our country, but working behind the scenes. Or he may have followed the storyline from the source material and was killed off a few years ago. At any rate, he is no longer a visible vigilant in Toobworld.
Captain Irving would not have been referring to the Captain America as seen in the Marvel movies, as he is active in the TV dimension of Marvel Toobworld (or ComicBook Toobworld to be more inclusive of other publishers' heroes.) He has not yet been seen in that dimension, currently on display in 'Marvel Agents Of SHIELD', but it is rumoured that he will be making a crossover to the small screen come the Spring (closer to the opening of the next movie, "Captain America: The Winter Soldier".)
It could be that another televersion of Captain America, played by Matt Salinger in the 1990's, resides in the dimension shared by 'Sleepy Hollow' and 'Elementary', but I think that would just complicate things. I think Salinger's Steve Rogers should remain in the Land of Remakes.
So that leaves the comic book character. 'Sleepy Hollow' is already over-burdened with its own mythology without me heaping any more on top of it.....