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A lot of threads on /fat/ seem to start with "I'm doing x, will it help y?" and I'm left wondering where x came from in the first place.
The short answer is yes, OP, doing frequent challenging leg exercises will probably make your lower body muscles grow. Is it the ideal way to do it? I don't know, but if you do it consistently over a long period of time you're likely to get bigger legs.
Interestingly Stan Efferding talks about doing 20 rep sets for other reasons. Something about the hormone response, or cellular response, or oxygen debt from the extreme demands of getting to that 20th rep... I'll have to look it up.