When emails are configured for HTML and Text, are both sent?

When emails are configured for HTML and Text, are both sent?

I have created all my emails to have both the HTML version and the text version.  When I send a test of the email to myself I get both versions.  Will people in my contacts list also receive both versions?  While I want contacts who don't want HTML email to be able to get a text email, I don't want the majority who I presume want HTML emails to get both.  That would be a bit spammy.  How do I handle this?

Thank you.