Aren't you still going to be paying that Core Technology fee once your FOSS non-profit app gets popular? I guess you would have to get that waiver but that's far from trivial[1], especially for an individual that just likes to publish an FOSS/free-as-in-beer app out of kindness.
If you're distributing your free app through the Apple App Store, no you wouldn't ever pay a core technology fee, even if you had a billion downloads.. it's a fee only for apps distributed by third party app stores.
[1] https://developer.apple.com/support/fee-waiver/