No. Your clients don't need to download an app, create an account, or buy a subscription plan. They click your link, choose a service, and pay with a credit or debit card, Apple Pay or Google Pay, right in their web browser.
A free client account adds a few extras: tracking projects across providers and messaging providers directly. A client on a paid Solo or Business plan also pays a lower booking fee. Guests and Starter members pay the standard 5.5%.