I suppose it would, initially at least. Turkey is also a good diet food. However, if you were to start eating it in the evenings as a way to help you sleep, I don't know if or when your body would eventually adjust to it.
tryptophan helps make you sleepy because it is an precursor for melatonine. The hormone which controls your biological clock. When it get dark your brain starts to produce a lot more melatonine and with this come the effects which are related to sleepyness.
But the concentrations of trytophan found in food are no were near enought to have a profound effect on melatonine levels in the brain. Even if you could ingest enough trytophan to have an effect on melatonine, i dont think you would want to. As there have been studies on this and the quality of sleep was severly lowered, peopl actually woke up every 2-3 hours and had bad nightmares.
The droozyness attribute to eating a large turkey dinner, which for americans happens a lot at festivities like thanksgiving is imho more related to the insuline action then to tryptohan.