You can only "Customize From Address" if the domain you're wanting to send from is added to your sending profiles. So. Yes. it's possible. But it's user-hostile.
Hmm. Do I have it right that you mean you can't send from e.g. "test@example.com" (using "Customize From Address..." then entering that address in the From field) unless another address for the domain "example.com" is set up as an account in Thunderbird (e.g. "hello@example.com")? If that's what you mean, then I don't think that's correct, as I just tried it and Thunderbird let me send the message despite me not having any account for example.com in my profile. I did of course get a response from example.com telling me there was no MX server, but that tells me Thunderbird went as far as sending it.
No I mean, I have many different domains.
So if I want to send an email from example.com, I have to add it to the sending profiles. This is fine, and usually done during initial setup. However, if I want to be able to send from a second domain, say, thisdomaindoesntexistasdadasd.com I need to go and add that seperatly for allow thunderbird to allow me to put it in the from addr. Further, when sending an email, I then have to select the domain from the drop-down, then edit. it's just tedious. Not impossible to work around, but also not worth the effort when the Fastmail UI handles it so much better.