Yes, but to insure safe remote starting of a vehicle with a manual transmission it requires a remote starter system specifically designed to be installed into vehicle's with a manual transmission. These systems install identically to a system for automatic transmissions with the addition of a couple extra outputs & connections (1 connection to the vehicle's parking brake and 1 connection to the vehicle's clutch activation wire) with a manual transmission compatibility setting. Known as a "Remote Start Ready Mode", this feature requires the driver to enable the vehicle to be remote started after the vehicle is parked; you can't just randomly remote start the vehicle anytime you want like you can with a remote starter on a automatic trans vehicle, you have to prepare the vehicle to be remote started...
While the vehicle is still running with the keys, the driver places the vehicle in neutral, set's the parking brake and then press and holds in the button on the remote until the dash lights flash (activation procedures will vary). Then the driver turns off the ignition, removes the keys, and exits the vehicle. When the remote start ready mode is set correctly, the vehicle will remain running while exiting the vehicle. Once the driver's door is closed the driver presses the button on the remote 1X which will lock the vehicle's doors (if equipped with factory power door locks, otherwise it will just shut down the vehicle) and it will automatically shut down the engine. The vehicle is now ready to be safely remote started.
In the event that the driver re-enters the vehicle without activating the remote starter, opening the driver's door will cancel out the remote start ready mode and the driver would have to perform the remote start ready mode procedure again.