No. There is no historical or cultural tradition linking Mexican women's attire—specifically skirts—to Cinco de Mayo.
The holiday marks the Mexican victory over French forces at the Battle of Puebla on 5 May 1862. It is primarily celebrated in Puebla (with parades, reenactments) and has become a broader celebration of Mexican culture in the U.S., but it carries no prescribed dress code.
Regional folk costumes (e.g., china poblana skirt/blouse in Puebla, tehuana dress in Oaxaca) are worn for cultural festivals, folkloric dance, or national holidays like Independence Day (16 September)—not specifically for Cinco de Mayo.