Can Margin bill a customer every month?

Yes, as drafts you check. Open an invoice and click Make this recurring, or add one in Books → Invoices → Recurring: the customer, the lines, the day of the month (1 to 28, so every month has it), the first month and, if it ends, the last.

On that day each month, Margin makes a draft invoice marked "Drafted from" and the schedule's name, and tells your finance team it's waiting. It never issues or sends one: someone checks it, changes it if they need to, and issues it. A month is drafted once, even if its draft is deleted.