My understanding is that when "output on connect" is selected, it will not start timers that would allow the node to signal if the "For" option is populated with a time.
I believe this would be good functionality to have, or at least some option to allow for it.
For instance I use the Events: State node to send a notification when say the garage door is open for more than 1 hour or if a node is missing for a day. If I restart in that time, the timer will not be reset and I will miss that notification entirely. I could workaround this in some other manner, but the pattern is very common at least for me and having the built in functionality would be really nice to have.
I do see it mentioned in the docs that it isn't supported:
"Warning: Output on Connect state changes will not start a timer."