I don't see any issue with doing so. Is there a reason you'd like to wait 2 seconds after connection before pairing? By default, the example uses the peer manager in order to take care of and store bonding information, so please check out the peer manager documentation to see if it meets your requirements.
Thank you for the clarification. This shouldn't be an issue either. Try setting the connection interval in your application lower, as this, by default, is set to be between 7.5ms and 4.0 seconds, but you can set the maximum to be 2 seconds if you'd like. This way the central will try to connect before 2 seconds has passed.
So you don't want to pair the devices when the mouse first connects to a central, but rather initiate pairing on the central whenever you'd like? I think this is up to your central, as the nRFConnect for Android application, for instance, can choose to initiate pairing to a connected device that is compatible, while a Windows computer will always automatically pair to a device identifying as a HID Mouse.
