Nope.
The controlling legal authority is the Fourth/Fourteenth Amendment, mandating freedom from unreasonable search. This is best viewed in the light of Katz v. United States, in which the Nine Worthies declared that searches into any area required justification, when a person had a reasonable expectation of privacy.
Your car isn't the same as your home, with the same protection. It is, however, more private than not. A search by a police officer may not require a warrant, but it does require some sort of legal justification, such as probable cause (facts and circumstances which would lead a reasonable officer to believe that evidence of a crime is present)
Speeding is evidence of speeding. It could possibly be evidence of drug/alcohol impairment, depending upon what else is going on. It could be a piece of circumstantial evidence for any number of things. It does not, however, automatically justify a search.
And I never charge DUI/DUID off of a vehicle search. I charge DUI/DUID off of my observations of the driver's manual dexterity and ability to focus and concentrate, and my observations of the vehicle in motion, and the alcohol/drug test justified by said observations. The mere presence of drugs does not imply the consumption of said drugs strongly enough to charge DUI, absent other evidence.
Why be a man when you can be a success? -- Bertolt Brecht