No. You may feel lightheaded after drinking alcohol through a straw from lack of oxygen but how drunk you get depends on the amount of alcohol consumed.
The straw itself would have no properties that would make you get drunk faster. The straw might make it easier for you to consume alcohol faster, though.
It depends on the size of your straw.... in order to ensure maximum intoxication you should use the largest straw available. If you only have childrens sized straws available you can use up to 15 at a time!