Does eating turkey make you sleepy? In a word, no. While turkey contains a healthy dosage of tryptophan, what makes people tired is two things: (1) Diversion of blood flow to the intestinal area to aid in digestion, robbing the rest of the body of precious blood and nutrients and (2) A rapid lowering of the blood's sugar level due to ingesting a large portion of high glycemic index carbohydrates with almost no fiber to slow the digestion down.
This "turkey makes you sleepy" belief is so prominent that even the great urban legends site Snopes has written about it confirming the belief as myth. Of course, they don't clearly spell out the impact of eating too many high glycemic index carbs on feeling sleepy, but having Snopes confirm this as myth is a source of absolute truth.
Incidentally, tryptophan doesn't make you tired. Rather, some of the tryptophan is first converted into 5-hydroxy-tryptophan (5-HTP) and some of this is then converted into serotonin. Serotonin is one of the chemicals in the body responsible for regulating mood. People who suffer from the common problem of depression tend to have lower levels of serotonin. Of course, the problem of depression is much more complex than this. For one thing, serotonin itself can either be reabsorbed into other forms while some is converted into melatonin. The melatonin is stored in the pineal gland in the brain until the body's natural timeclock decides it is time to release the melatonin, which suddenly floods the body with intense feelings of needing to sleep.
Since only a portion of the tryptophan from the turkey every becomes melatonin and since the melatonin would first be stored, it is extremely unlikely that turkey makes you tired.
Finally, for those suffering from mild depression of various sleep behaviors, taking 5-HTP supplements can actually help. 5-HTP has been clinically proven to be more effective at treating mild depression than Prozac. Of course, mild depression is mild. Anyone suffering from other more severe forms of depression should continue to follow their doctor's advice.