Hello, @LBH, yes, new to the forum.
Determined, I did some even further digging…
First, I believe Ableton refers to this feature as "Resume". You can resume with the keyboard shortcut Shift + Space. I find it really useful since it behaves just like a play/pause button on a tape deck. Play picks right back up from where you hit pause instead of skipping back to the beginning of the clip or loop (which is also very useful, of course!)
I finally stumbled upon a post in the Ableton forums that explicitly outlines the Ableton-specific control messages that supporting controllers can use to communicate transport instructions. Of course, the Keylab supports these messages. Unfortunately, there is not a control message for "Resume". I think that settles it. Until Ableton adds a new control message for resume, Arturia (or any other manufacturer) could not support that feature.
Alas.
Thanks for the reply!