Is it possible to correctly identify presence of Y chromosome with external physical test only?
No, an external physical examination would be inconclusive. The reason is the TDF
gene. To be more specific, if a person has XY and the gene is not active then the subject
would have a female appearance. Also we cannot conclude that a person has a Y
chromosome even if it has penis because that gene could be transferred on the X chromosome.

Here is a reference: http://en.wikipedia.org/wiki/Testis_determining_factor.