I've tried it before a few years ago. It has an added feature known as " Placebo Effect " that isn't in Logic
In reality you can't tell what DAW a track was mixed on as it's very much down to the skill of the mixer and/or master engineer. If you want a more analogue sound there's plenty of plugins for other DAWs that do something similar, for example Studio One has it built in and you can choose to turn it on or not.
The only real benefit might be from a workflow point of view ....if that's how you prefer to work.