Presumably, since alcohol can be absorbed through mucous membranes. However, all these answers are obviously from people who don't know the least thing about anatomy and physiology-or tampons.
First, alcohol ingested into the GI system is absorbed directly into the blood-there's no such thing as "bypassing the liver" Alcohol is metabolized by the liver through the blood circulating through the liver tissue at a fairly steady rate so your liver only has to do with how drunk you get in the sense that it can only clear the alcohol so quickly.
Alcohol absorbed through the mucous membranes will get you drunk more quickly but the degree of intoxication is still directly related to the amount of alcohol absorbed. Since the highest absorbency tampon only holds 15-18g of fluid, you aren't going to be getting that much alcohol.
Since the alcohol measured in a Breathalyser test is diffusing out from your blood, any method that causes intoxication will cause a positive Breathalyser because to be intoxicated the alcohol has to be in your blood. Duh.
I suspect the orifice the tampon was inserted into would be quite irritated, though.
And last I heard, there is no law saying men can't purchase tampons.
There is such a thing as alcohol enemas, you could look into that, haha.
And one last thing-you aren't really trying to find some viable method of drinking and driving without risk of getting arrested, right? You know getting arrested is like the lowest risk thing that can happen if you drink and drive 'cause you're smarter than that.