Possible to publish Android app that uses Jetpack Compose to Play store?

It looks like there is a new way to build UIs, called Jetpack Compose

I would describe it more as "upcoming".

I'm familiar with iOS world, where a beta version of Xcode cannot be used to release a live app in the App Store.

That's goofy.

Is a similar thing true with Android?

No.

Or could I use a canary version of Android Studio along with Jetpack Compose and then publish to the Google Play Store?

Yes.

There is a ton of stuff to learn on a new platform, and I'm not sure I want to invest in learning APIs and methods that are about to be obsolete.

Conversely, please bear in mind that right now (July 2020), Jetpack Compose is almost completely undocumented. Its APIs are changing frequently and will continue doing so into 2021. Right now, it is not even really aimed at experienced Android developers, let alone newcomers.

Moreover, the "APIs and methods that are about to be obsolete" will be used for years to come. Compose is slated to become stable in 2021. Let's pretend they achieve that on January 1st (a preposterous schedule, but, we're pretending). It's not like on January 2nd 2021 all the world's Android code will be using Compose. I would be impressed if it were the majority choice for new development on January 2nd 2023, just because a software development ecosystem is slow to change. For existing code, rewriting it in Compose will be a long-term process taking years, and some projects will never make the switch.

If your objective simply is to play with Android on personal projects, and you want to go with Compose now, you are welcome to do so. If your objective is to work on Android professionally, you will need to know about fragments and views for the foreseeable future.