Yes. Pretty sure there is an ASA case play on this, or a similar situation, but the concept is sound. The interference actually kept F6 from doubling off that runner; batter is already out by the infield fly rule.
I don't think it matters that the IFF was called first. Just like we can (and must) assert that rule if it was misapplied by not calling it in live time when it obviously applies, so would the application call for that decision after the interference.
I always try to remind people when discussing the infield fly rule that it is half judgment and half a rule application; we do not change the live judgment that it wasn't an infield fly (not catchable by an infielder with ordinary effort, or a line drive vs fly), we do change the misapplication of the rule (forgot how many outs, forgot where runners were, forgot pitcher and catcher are infielders, etc.). That would still apply here, if the ball was made dead before it was called.
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Steve
ASA/ISF/NCAA/NFHS/PGF
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