A 'not' option in managing processor or networking times is not available but you can work around it, sort of:

Set the overall daily to 00:00 to 00:00
Enter Sunday 00:00 to 00:01

That will give just 1 minute, the shortest since any equal start/end times is interpreted as always on. Make sure to set the Activity menu option to Network based on preferences.

There's a never fixed rounding bug. For that see the start Here FAQ's which has a networking sample discussed in detail.

edit: spelling

Yes the cache/additional buffer has to be increased to bridge the longest period that a client is not allowed to connect. BUT, if you set in the client or web profile the option Connect about every 1.25 days for instance the client would fetch the appropriate amount and a little extra in case the work ends up running faster.

Note that once one starts using local prefs they override web prefs and unexpected behavior can be experienced. From thereon look in the local prefs what's in effect.