It actually did in TestFlight, but they removed `apk` from the included filesystem as part of the app review process. It's pretty easy to go onto Alpine's website and get a different filesystem to import, though ...
Apple's restrictions resulted in a pretty severe reduction in functionality of the app. Many of their how-tos still contain apk commands which no longer function.
Simply go to the [0]download page, look for "mini root filesystem" and download x86, or simply click this [1]link
Upload this to your iPhone. Then in the iSH settings find the "filesystems" section and click "import".
[0]: https://alpinelinux.org/downloads/
[1]: http://dl-cdn.alpinelinux.org/alpine/v3.12/releases/x86/alpi...