Yes, there were drafts but often there were desertions as well. Often states were unable or unwilling to fill their quotas on men so you had an enlistment process. In this process, people who were usually officers from the areas they were recruiting in, went from town to town to get volunteers. Often they were able to offer pay because they were authorized by either Congress or the state and that unit would then provide the pay. Who was accepted into service depended on who was doing the recruiting. Some, such as Daniel Morgan, had rigid tests for anyone wishing to join his riflemen. Others would take anyone who could walk and take orders.
So, to sneak in as a woman you'd need to know where the recruiting was going on and try to sign up with an officer who was known to be lenient about who joined them. It would be best to tell them you were a laborer without a home, from the Boston of Philadelphia area , who made a living by doing whatever the boss wanted. Maybe even throw in a story about how a redcoat in Boston had you cut some wood and never paid you and you wanted revenge.