I think the vast majority of the incestuous undertones were intentional and that spn is the 7 Minutes of Incest Show, if not from day one, then certainly at least from season one. Kripke and Gamble both called it "the epic love story of Sam and Dean" and Jensen has called it a love story about two brothers. The number one major theme of the show over its whole run is the way love, abuse, and horror in families run together and interact, and an act of vertical, nonconsensual incest (Mary and Azazel's kiss) is the first domino through which the entire rest of the plot occurs. Kripke was asked by Standards and Practices if he'd be willing to remove it and he declined. That suffocating feeling of someone loving you enough to do anything for you, but also anything to you, and how that's an unacknowledged aspect of familial love--all of that is all over the text and has to be intentional. It's too blatant, omnipresent, and barely even given plausible deniability, to not be.
That said, I also think there was no intent at all that Sam and Dean be interpreted as actually banging each other or even interested in banging each other. The risque jokes are just risque jokes. They practically write themselves even had both the writers' room and the set not apparently been inhabited mostly by people with the sense of humor of twelve year old boys (which I'm not complaining about--I too have the sense of humor of a twelve year old boy and find most of the jokes hilarious). The weird interest in each others' sex lives is just the same over-investment they have about every other aspect of each other's lives. And the more serious romantic/sexual overtones imo are there to reinforce the platonic/emotional love story, not tell a separate one.
R.e. how much did the general audience (GA) notice it, I have no idea tbh. My guess is probably not much, because the GA is there to be entertained, not think too hard about every little detail like we do in fandom. Spn is a very vibes-based show and one can easily absorb the vibes for entertainment purposes without thinking too hard about what they mean.
And to be blunt, people in general have a metric fuckton of practice not noticing irl incest while pretending to be vigilant about and horrified by it, so why would they notice it in a fictional setting where the love between the (emotionally) incestuous family members is ultimately redemptive and always saves the day? That's a pretty hard disjuncture to face squarely imo. Not looking away is a learned skill that most of us have no specific reason that we know of to learn, and it's in many ways an awful experience learning it, so why would most of us bother? I've never specifically asked a GA member about the incest piece in particular, but my spouse, who is a GA member, didn't notice that spn is particularly rapey and didn't notice that Lucifer had canonically raped Sam, even though Spouse has a long and sometimes complicated marital history with a rape survivor.
Anyway, thanks so much for the ask! I'm always very interested to hear the opinions of others, so Nonny, you and anyone else who feels like it are welcome to add on in reblog.