Yes. Three counters are free, and Premium raises it to eight.

Why does the number take a while to change?

Discord only lets a channel be renamed about twice every ten minutes, so the counters refresh every ten minutes. Every bot has the same limit.

A Discord member count bot

Show live stats at the top of your channel list, like Members: 1,204. Tick the stats you want on the dashboard and word each one your way.

The channels are locked voice channels: everybody can read them and nobody can join.

Open the dashboard, go to Counters, tick the stats you want and word each channel name however you like. {count} is where the number goes.
Save, and within half a minute the channels appear in a Server Stats category. They're locked voice channels: nobody can join them, everybody can read them.

Is it free?: Yes. Three counters are free, and Premium raises it to eight.
Why does the number take a while to change?: Discord only lets a channel be renamed about twice every ten minutes, so the counters refresh every ten minutes. Every bot has the same limit.
What permission does it need?: Manage Channels.

A button panel that opens private support channels, with transcripts.

Ban, kick, timeout and warn, with every action kept as a numbered case.

Rules that deal with spam, bad words, links and raids without a moderator.

Greet new members with a message and a picture card, and say goodbye.

Let members pick their own roles with buttons or emoji reactions.

Give every new member a role the moment they join.

Free, and nothing runs until you switch it on.