For this task, it seems Mainstage would be a better fit than Logic. However, I cannot really recommend doing that. Modern computer OSes have a large number of processes running in the background, unpredictable disk access or memory allocations going on, nearly unpredictable CPU power saving automatisms, unpredictable scheduler granularity, etc. In addition, you have a multi-purpose system architecture that is not optimised for signal flows as important data can easily fall out of cache lines or even be scattered in memory. You can partly compensate for all this by running relatively large buffer sizes and using safety buffers, in short, by introducing a lot of latency. But even with this latency added, the system will still be a rather big safety margin away from performing optimally. Modern plugins are also not always optimised for ultra low latency and add even more to the total in-to-out latency.
That said, it's not impossible, but I would sweat blood during a show that I mix with a general purpose setup like this. And I wouldn't even try it without first having set up an absolute minimal OS installation and proof running that many times. You'd have to live with total monitoring latencies of more than 10 ms, which will definitely confuse drummers and bassists enough to ruin any groove.
Modern mixing consoles got a lot cheaper and come with tons of features that are very comparable to the mixing abilities of DAWs. Take the Behringer X32 for example. It has already started to reform the market and will trigger a number of future products with many channels, high routing flexibility, high quality internal plugins, digital stage boxes, very low latency and all that for relatively little money. The golden times of digital mixing are still ahead of us if you ask me. Getting a Mac (or PC) based rig that would perform nearly as well (and then not quite) would cost much more.
My live setup consists of a digital stage box that I also use as remote controlled monitor mixer and a digital FOH mixer. I use logic only for recording the performance. I'm very happy with this setup and I don't feel limited by it at all.
Cheers,
Jazz