I don't remember doing that when I was a kid. I hardly remember speaking at all, though.
If my brain is completely frazzled/fried (overloaded), and someone's talking in my face and it sounds like a lot of wah-wah nonsense, there is an urge to mimic back at the person. I usually refrain, though.
As far as things like the microwave beeper, or my cat, iPod alarms, and jingles on TV, I do tend to parrot those back. Not sure if that counts as echolalia. And, also movie & TV lines, as others have said. And sometimes, randomly, complicated chemical names. I.e. "para amino benzoic acid" "chloro methyl phenyl triazolo benzodiazepine." (As a kid I was really good at figuring out how to pronounce complicated, new words.)
A bit OT: I've wondered if the ability to 'absorb' the aesthetic of something is an autistic-specific strength. Like, an accent, the way someone moves, or even the 'character' that inanimate objects can have; and even the 'shape' of calculus, and logic, and such.