Bah! A parenthetical by any other punctuation is still a parenthetical.
Not really, each punctuation marks has certain associations. Parenthesis are designed to yank you out of the current conversation to impart specific information—which is why it's frowned on in fiction. Commas work, without much significance one way or the other, while em-dashes denote something significant, something worthy of special note, it draws the eye. I frequently use them for a brief aside which foreshadows a major event to come in the future. Readers may not read much into it, but because it's marked in such a way, they tend to pay more attention to it, so it's likely to remain in their memories longer than a simpler aside.
The key, though, in all of this, is to NOT pull the reader out of the story. If you can't figure out a way to include the information in the story, then it usually belongs on the cutting room floor as immaterial to the story. If the aside isn't essential to understanding or advancing the story, then it's just not worth the effort.
A good example of this is how you might spell out abbreviations in parentheses in an email, but in fiction, it's cleaner to include the information in dialogue, as it's 'more natural' coming from the characters rather than from the author himself (re: Author Intrusion).
"We're from NCIS."
Tim sighs. "The Navel Crime Investigative Services."
The suspect rolls his eyes. "Couldn't you just say the damn Navy cops?"
"If I could, I would. You won't believe the number of times I've got to explain who the hell we are. NCIS doesn't just roll off the tongue like shouting 'POLICE!' does."