Yes, through custom configuration of payload and topics the MQTT Transmission module in Ignition can send data to Factbird.
The MQTT Transmission module from Cirrus Link Solutions acts as an Ignition tag to MQTT Sparkplug bridge. It enables listeners to be attached to Ignition tags which then wait for tag values to change. Factbird does not support the Sparkplug specification (Does Factbird Support the Sparkplug MQTT Specification?), but the MQTT Transmission module does support custom topics and payloads. You might need to use MQTT Engine to customize the payload and topics.
Factbird can not provide technical support for this setup, instead we refer to Setting up Kepware.