In the Google Play flavor [1] and with ntfy.sh, yes. If you use a selfhosted server or use the F-Droid flavor [2], then no. In those cases a foreground service with a persistent connection is used.

You can find more info on the configuration page for a self hosted server [3].

You may want to check out this question in the FAQ too [4]

You can also turn off publishing to FCM for ntfy.sh on a per-message by message basis [5].

[1] https://play.google.com/store/apps/details?id=io.heckel.ntfy

[2] https://f-droid.org/en/packages/io.heckel.ntfy/

[3] https://ntfy.sh/docs/config/#firebase-fcm

[4] https://ntfy.sh/docs/faq/#why-is-firebase-used

[5] https://ntfy.sh/docs/publish/#disable-firebase