Does Ezreal Q consume Rapid Firecannon proc?

I've been building Essence Reaver/Shiv/Rapid Firecannon/IE on every adc that can use cdr. The build feels so amazing. I'm not sure if it's optimal or not, but when you're ahead you are a god.

I played a couple Ezreal games with the build (feels best on him, 2nd only to Lucian). I can't tell if Rapid Firecannon is consumed by his Q. I know shiv procs it, and RFC is worded the same way ("on next basic attack"), so I was wondering if it's an on-hit effect (like shiv) or an on-attack effect. If it doesn't work on his Q, it would be pretty awesome, since you can poke with Q and still maintain the range to poke with a longer auto.