I mean, yes. I can remember what it was like to watch anime for the first time. Though, I was five, and didn't know that it wasn't meant to be different from the other cartoons. I did realize that later, sure, but only because it wasn't episodic, which made it better than the other shows I was able to get in my isolated town.
If you mean knowing that it's anime...well, "refreshing" was the best way to describe it. TV that was actually interesting. Kid stuff wasn't interesting for the same reason it wasn't as good as anime as a kid, adult stuff wasn't interesting because they don't try to appeal to non-adults, teenager stuff was...unfunny and alienating, mostly. It was a unique place where you get see what you wanted without being confined in a demographic.
This was more reflected in my manga list than anime list, though. Most of the anime I watched was what my friends watched. My old manga list runs the entire gamut, having things like Ane Doki, Suicide Island, Hohzuki Island, things that I wouldn't expect to get elsewhere.