Does VT have the ability to publish data to an MQTT broker?

Short answer: No. The MQTT tag is a subscriber only.

But, if you really want to do this, you can roll your own by writing a Python (or whatever) script that can send SQL queries to the tag database via ODBC, then publish the data to your MQTT broker. You'll need the Remote Data Access feature as part of your VTScada license key.

We have bee successfully using the free Mosquitto MQTT Broker with our native VTScada MQTT Client.

FYI, some other SCADA platforms seem to offer a native MQTT publisher but, in fact, are also using a third party Broker/Publisher product and require you to go though that manufacturer for support. Read the fine print.