Yes. Donors can select the monthly check box to give automatic monthly payments.

PayPal attempts to collect recurring payments from subscribers on the day after the previous billing cycle or trial period ends. Billing cycles can be daily, weekly, monthly or yearly, depending on the terms of the original subscription. 

You can view examples of how Weekly, Monthly, and Yearly billing cycles are collected at our PayPal Developer site here: How Subscription Billing Cycles Work.