??? Sitting here at 41 weeks pregnant and no signs of labor, and as someone who thinks 12 cloves is a "a good start, but don't we have more garlic?" for a recipe I'm finding it very difficult to worry about garlic causing contractions.
And a single clove as a vaginal suppository isn't going to be more potent than eating a ton of raw garlic. The effects described all relate to the chemicals in the garlic entering the blood stream. There is nothing in that article about effects on mucous membranes except possible stinging from exposure to the juice.
And of course garlic will have an effect on bleeding, the main use for oral garlic supplementation is as a blood thinner. But I'll believe that sticking it in your vagina has that result only after someone does a study on it.
Besides, if you catch the yeast symptoms soon enough, you'll only need to use a garlic clove suppository for one day. Quite a difference between that and daily supplementation.
(Ingesting large amounts of anything is a bad idea.)