No, because 1) FastMail doesn't make money through advertising so they have no incentive to read your mail and 2) if you pay for an account with your own domain, you are not locked in, so if they start doing something you don't like, you can migrate away without telling all of your contacts to use some new address.
These benefits are broadly true of most paid-for private email hosting providers.
One thing though, customers like me use FastMail specifically because they aren't in the Privacy Farming business like Google.
If they ever do start privacy farming then I'll be incentivised to move my domain to a separate supplier.
If I didn't care about that I'd just be using Google's "free" service already. So FastMail are incentivised to protect their business and to not compete head on with Google.
They don't offer a free service, they offer a paid service, you are indeed the customer. They also don't have another service that even could pull the data from FM.
