Consider the following scenario:After overhearing from a public telephone what appeared to be arrangements for a drug transaction, a police...

The answer is unclear.  It may be yes or no, depending
upon several factors.

First, the search of a closed
container within the passenger compartment of a car is NOT the same as the search of the
car itself.  The suspect here consented to a search of his car.  Arguably that consent
does not extend to the search of closed containers in the car.  Consent will be an
issue, and it is likely to go in the suspect’s
favor.

Second, the search could be justified as a search
incident to lawful ARREST.  Except there’s a problem with that justification.  The
suspect isn't UNDER ARREST in the fact pattern.  Your professor will take a very dim
view of your adding facts to his/her fact pattern, to say nothing of the fact that
without the drugs, the officer may not have adequate evidence to actually arrest the
suspect.  (I think we can all agree that the traffic stop itself was pretextual, lawful,
but probably does not give the officer the power to arrest the
suspect.)

Third, and probably most important, the officer
could try to justify the search because he had probable cause to believe that the
suspect was transporting narcotics.  He would base this probable cause on the
conversation that he overheard.  Overhearing a conversation while in a place that is
open to the public, that a member of the public could have overheard, IS NOT an illicit
search in itself.  This evidence could be the basis for probable cause and probable
cause would give the officer a basis to search the container in the car.  So the officer
would then have the suspect’s consent to search the car and his own probable cause to
search the container within, making both searches lawful.  The ultimate question will
be:  Was the overheard conversation adequate to give the officer probable cause to
conduct a search of the suspect’s vehicle AND ANY CONTAINERS
THEREIN? 

If the probable cause is lacking, the consent
likely does not extend to the container and the search will not pass Constitutional
muster.  Hence, any evidence recovered will be inadmissable due to the exclusionary
rule.