A good percentage of lolcows are either full time or part time grifters who lie and misrepresent themselves intentionally for money. So if by "self aware" you mean "do they understand they're full of shit", then yes a lot of the grifters do know they're full of shit.
More generally, I think its also possible to be very self aware in one aspect or area, and very tunnel-visioned in others. But that usually requires compartmentalization, and lolcows by their very nature are people incapable of compartmentalizing. Lolcows become lolcows because they can't compartmentalize the crazy and keep it private.
To your question, yes self-aware lolcows exist, but its only certain types of lolcows. mainly the grifters who intentionally try to be cows for attention and money.