What you want to do is totally possible - but Logic might not be the best platform for that - not my area of expertise (I have a fair bit but not applied to using a DAW live).
My concern in general is that you are still going to need some way to cue that DAW - you couldn't just start a show and stop at the end however long that takes, so you will still need a midi device of some type - potentially a pedal board? You are also relying on a computer behaving perfectly for all that time............I'd be very cautious of that! You would need to turn off everything that was not related (all those little routines that go out to the net or the wifi network just saying "I'm here") so no cycles were lost checking Adobe cloud or something else stupid - so you would need to be sure you had a robust routine to make sure that Laptop (I'm typing this on something very similar) was just doing the job you wanted for the show and absolutely nothing else. That kind of means your safest path would be to have it devoted to your show and not have a life as a general tool. You can't have any stray "boings" due to any system events - yes, it's all possible, but what makes something like a Helix floor (which is the most obvious choice for live) so reliable is that although it's a computer, it is purely dedicated to making sound and a OS that does nothing else. Your Mac OS is doing tons by default that has nothing to do with the task at hand. I know people are doing it for Keys and even running a lighting rig, but those who are having 100% success are either keeping that machine for that one job, or have either personally or through a very tech savy contact created a routine (script or program) for setting that computer to do as little as possible that is unrelated while it does that show. I've seen something as simple as a powerpoint presentation go terribly wrong many times due to that computer pausing to do something "in the background".
I've also never used Alberton Live, but I've heard it's the most suitable for live shows.........but you probably already have way too much time invested in Logic I suspect?
So outside issues of latency etc, you are expecting a robustness from the system that would trouble me personally!