Will my Bluetooth headset be able to play audible warnings from ForeFlight Mobile?

If your headset supports "music" via Bluetooth then audible warnings will go to your headset, along with any other sounds the iPad is playing. Audible warnings will not work with headsets that are only offering phone connectivity via Bluetooth.

A simple test is to tap on MORE > SETTINGS and then under Alerts tab toggle the Speak All Alerts switch OFF and then back ON.

If you need to adjust the alert volume, when the alert is playing you can press the Volume Up or Volume Down toggle on the side of the iPad or iPhone.

NOTE: The iPad and iPhone can only output audio to one device at one time. If you are wanting to hear the alerts on multiple Bluetooth headsets, you can consider using a Bluetooth headphone splitter.