... being a manager and staying late with your developers, your first priority shouldn't be riding them but play a support role.
Absolutely. There's the very basic support, like ordering the food and making sure the cleaning people don't turn off all the lights, which is very useful. But more importantly, being available when something comes up that the developer needs help with. Question about requirements comes up? The manager can call the functional guy and ask. Problem with access? The manager can call up the sysadmins and get the ball moving. It's pretty rare that something is so completely cut-and-dried that the developer can work late hours with no outside support to get it done. When that outside support is needed, having the manager right there to get the help that is needed can be a great help.