I'm on macOS 15.4 on a 2021 M1 Max. I haven't rebooted for months.

Is it possible for me to update to whatever was released just before "Tahoe", or will it just put me on that now?

Yes you can still update to 15.7.3 the usual way in Settings

It'll present you the Tahoe upgrade but underneath in small print it'll show other updates, which you have to then open and manually select the 15.7.3 update

And you really should keep up on the point updates because there's been a ton of major security patches since 15.4