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