It does not. The guest that answered it could show up as a methamphetamine positive is completely wrong. This will not happen. Many years ago this was a possibility but not in today's labs.
NyQuil can cause false positives for Meth/Amphetamines & opiates.
If anything there may be along with alcohol in nyquil a drug called psudophedrine and that could show up as a methamphetamine.