It's the kind of 'low bandwidth' you'd see with analog telephone modems. A single JSON request-response over TLS would take many seconds.
With the current satellites, yes, if they think they have enough capital (at least many hundreds of millions) to launch a new clean sheet of paper design LEO network using the existing globalstar L/S-band spectrum licenses, they could implement something better.
The value of globalstar is not in the existing satellites and earth stations, which are pretty much trash at this point for any modern use except very low data rate M2M data in certain geographically restricted areas. The value is in the existing LEO network operational licenses.
I wouldn't be surprised if the current Globalstar network is so limited it wouldn't even do voice.