No, it is not possible. That is because to use the self timer you must select one of the two Self-timer drive modes. To shoot bursts you must select the Continuous drive mode. You may only select one drive mode at a time, so you must choose one or the other. The same is true with a wireless remote, since that also requires using one of the Self-timer drive modes.

One workaround you have is to use a wired remote with a built in intervalometer such as the Canon TC-80N3 or generic equivalent. Plugging a wired remote into the N3 port allows you to use the camera in any drive mode, since the wired remote functions exactly as pressing the physical shutter button. You could set the timer in the wired remote to have a 10 second (or 10 minute, or whatever time you choose) delay before activating the shutter. If the camera is set to Continuous drive mode and set to a specific shutter speed, semiautomatic, or auto mode you can set the set the timer to hold the shutter open for whatever time you desire and the camera will fire in burst mode as long as the timer is sending the full button press signal to the camera, just as if you were physically holding down the camera's shutter button.

I've been using the generic model linked above for over four years and it has held up fine.

Another option is to shoot tethered to a computer via EOS Utility.