Yes. Your payment processor doesn't matter — Stripe, Authorize.net, PayPal, Shopify Payments all work the same.
We track everything through Shopify discount codes, so the only requirement is that you're using Shopify's native checkout. When Shopify marks an order paid and the order used an ambassador's code, the commission is recorded.
Paying your ambassadors is separate and entirely up to you: ConvertOut tracks balances, you send the money however you like. You can even change what payment details ambassadors are asked for in Settings (the prompt says "Enter your PayPal email" by default).