You will lose some functionality, but a browser can get the slides. However, as far as i know, you must have an active projection screen. If your laptop screen is big enough, you can send the slides/videos/etc to a window on the laptop. Then the browser view will work, but won't get videos.
If the OpenLP projection window fills the laptop screen, then you can use a second browser device to manage the service. It's not ideal, but might work for you.