As long as you're on the same network and your computer is set to wake up for network access, Jump Desktop will be able to wake up your computer and connect to it. Very soon we'll also add support for wake on lan from the internet.
However for reliable remote access, we recommend setting your computer to not go to sleep:
On Windows open up the Power Options applet in the Control Panel and make sure your PC is set to not go to sleep when connected to a power source.
On a Mac open up the Energy Saver options and make sure it's set to never go to sleep in the Power Adapter section.