Is it possible to trigger an event to run when I open a TouchBar group?
I currently have a group that opens a faux MIDI keyboard but the program needs me to press M to activate input first. I needed to the button that opens the TouchBar group to send M to the program when I open the group.
Yepp! Create a conditional activation group for this using the bottom left plus inside BTT (chose Active Touch Bar Group in the setup menu), then go to the Named & Other Triggers and search for "Conditional Activation group activated" 
Edit: maybe easier: select your Touch Bar group, and hide it (right click on it, or hit ⌘D). Then, create a new button with associated action "open Touch Bar group with name" and as second action using the big plus below "send keyboard shortcut to specific app" 
The second solution is perfect, thanks!