Is it possible to transcribe live calls with asterisk?

All of the components are present to be able to do so. It’s up to you to put the pieces together. ARI has the ability to snoop on a channel for example[1] which can be used to passively fork audio. Once done ARI also provides external media[2] functionality to direct media outside of Asterisk to an application. What happens there is up to you. There is an example of an external media implementation on Github[3]. If you’re wanting a complete out of the box solution though, then that doesn’t exist from the project. We’re a toolkit, it’s up to you to use what we provide to do what you need in many cases.

[1] Channels - Asterisk Documentation
[2] Channels - Asterisk Documentation
[3] GitHub - asterisk/asterisk-external-media