The Great Gatsby, if pressed

Could you please tell me if in this extract from the chapter Four of The Great Gatsby the phrase "if pressed, they would confess" means "if they were pressed" (hypothesis) or "when they were pressed" (reality)?

and their last names were either the melodious names of flowers and months or the sterner ones of the great American capitalists whose cousins, if pressed, they would confess themselves to be.

Thank you.