No it doesn’t as the plugins run on your system and uses your internet to send orders.
I came across this video on youtube video
Where this person has taken the plugin usage to next level(hats of to human ingenuity).
The guy is running plugin on chrome in some cloud and then even when he turns his system off, the chrome keeps running on cloud and plugin keep running and taking trades.
The key takeaway here was that now I can run chrome on a Free remote server where I can keep things running on auto, and then check the progress/status on my mobile anytime anywhere(via app, I can stop/deploy strategies and the chrome will keep taking my trades) .