I understand what you mean. As far as I know, doors tend to close every time a new round starts, and they also have a "Fire on close" key. So in theory, if used with the "Toggle" flag enabled and "Delay before close" set to "-1" (And maybe also with "Start opened" flag enabled as well, not sure), you can trigger entities whenever a new round starts.
I've just tried to construct an entity setup that involves this func_door trick. What it's supposed to do is to disable a trigger_multiple when a player touches it, and then enable the trigger when a new round starts. I tried disabling the trigger itself with a multisource set as its master, also I used a trigger_auto to enable the multisource on map start but the multisource seems to stay disabled for some reason. Not sure if it's even possible. But it's most likely my fault as I've never been good at setting entities up.
However, if you somehow manage to find a workaround, feel free to share it.
Also, since you're new to goldsrc mapping, I suggest you to read through all or most of the tutorials if you haven't already. This could help you alot.