Torrenting only works if the peers can connect to each other. If you dont have a port forwarded, then you can only connect to other peers that have a forwarded port. At least one of the 2 parties connecting to each other needs an open port for the connection to happen.

If you are on a public tracker it can happen that a torrent is shown to have multiple seeders, but if you try downloading it without having an open port it won't work unless at least one of those seeders has their port open. This is mostly a problem on public trackers, since many private trackers enforce their members to have working port forwarding.

So it is technically possible to download torrents without working port forwarding, but only if enough other other peers have port forwarding set up on their end and your tracker doesn't (rightly) ban you for it.

Does the client automatically do it?

If you aren't using a VPN then most torrent clients will automatically set up port forwarding on your router using Upnp. Unless Upnp is disabled in your routers settings. If you are using a VPN you usually need to set up port forwarding manually, but there are some vpn clients that do it automatically

Edit: this article explains it better than me: https://protonvpn.com/blog/port-forwarding/