I see the problems with that, but I also see issues with it as well on the automation side.
Before we get into it, I wanted to note that if a download error occurs and it's not within the custom app itself (where it would probably pause automation if it were) the custom app doesn't get logged to the work report if it fails to download and moves on. So there is a way to tell if it ran correctly or not as far as d7II can tell.
Next the problems with stopping it in automation.
Leaving it checked would have d7II infinitely try to go back and run those again. Each time d7II finishes an app it looks at the sections again (left to right, top to bottom) and runs the first check it finds, this way you can add/remove items on the fly during automation. Might not seem like a problem in cases where network connectivity is restored later and it works, but the problem would come in if the custom app download is broken (either invalid/changed download link or the 3rd party servers aren't accessible). d7II would just continue to try and try but never be able to complete.
Possible solution now if you wanted to make this happen is to add to each of the custom apps profiles, to have them wait for processes of the various browsers (ie, chrome, firefox, etc) This would pause the automation to wait for you to try to download the app manually or close out the browser before moving onto the next app. Now this would copy those app profiles so any of the default apps wouldn't be maintained by Foolish IT anymore they would be in the Users Custom apps.
I'll point this out to Nick as well and see if there is any Nick Magic he can think of programing wise that would work best in this situation.
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& long time tech friend of Nick & avid Foolish IT product user since before Foolish IT was even created!