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No.

1) Before macOS boots, LittleSnitch ("LS") does not have any ability to block hostnames, e.g: on every boot, any modern Apple product ignores any manually-configured DNS IP and attempts to phone-home

2) Allegedly, this user profile information is stored locally (so LS wouldn't see any outgoing connection attempt to Apple servers)

3) LS does not block DNS-resolution, only IP-connection (i.e. your ISP sees all DNS queries, whether you click `ACCEPT` or `DENY` when LS popup asks)

4) If you're using LS with intentions of primary DNS blockage, you have failed; try pi-hole (or other local hardware DNS resolver); use physically-dedicated hardware (e.g: Raspberry Pi) to run your PiHole, not a Docker/Prox/&c

5) I am investigating another user's comment on using TLS certs to DENY-all DNS, but need to research further on this (new info to me!)

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The processes aren't (as far as anyone knows) slinging data over the network.
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