Is texting required for Apple Watch fall detection?
None of this data is sent as an iMessage or SMS.

If I have a talk-only phone plan without texting, for example, would the location still be transmitted as part of the emergency call?

If you have a talk only plan with no texting (do those still exist?), it won't be able to send GPS location data at all.  How would it? &quot;Talk Only&quot; means just that - talk - there's no data whatsoever so it couldn't send location data.  It's a moot point anyway.
The way fall detection works is that after a fall has been detected and you haven't responded, it makes a voice call to the programmed emergency number and plays an audio message that includes latitude and longitudinal data.
From Apple Support Use fall detection with Apple Watch

When the call connects, your Apple Watch plays an audio message that informs emergency services that your Apple Watch detected a hard fall and then it shares your current location as latitude and longitude coordinates.

So, to answer your question, yes, the location would be transmitted, as audio as part of the emergency call.