After reading wiki further (which has quite an extensive description), it looks it is somewhat possible:
Injections of acetylcholinesterase inhibitor, which effectively increases available acetylcholine, have been found to induce paradoxical (REM) sleep in humans and other animals already in slow-wave sleep. Carbachol, which mimics the effect of acetylcholine on neurons, has a similar influence. In waking humans, the same injections produce paradoxical sleep only if the monamine neurotransmitters have already been depleted.
Based on the last sentence (and provided the Carbachol mechanism of action is the same), it looks like you can't enter REM sleep if you aren't 'tired' enough.
Injections of acetylcholinesterase inhibitor, which effectively increases available acetylcholine, have been found to induce paradoxical (REM) sleep in humans and other animals already in slow-wave sleep. Carbachol, which mimics the effect of acetylcholine on neurons, has a similar influence. In waking humans, the same injections produce paradoxical sleep only if the monamine neurotransmitters have already been depleted.
Based on the last sentence (and provided the Carbachol mechanism of action is the same), it looks like you can't enter REM sleep if you aren't 'tired' enough.