No.
The Form creator can set the Google Form either to collect email addresses of respondents or not collect them.
If you are signed in to Google then just under your email address there is a little icon of an envelope and the words "Not Shared". That means the Form will not record your email address.
It's not something they can fake. It's set automatically when the person creating the Form ticks a box to set whether or not email addresses should be collected.
If you are not signed in to Google, the message is different. It says,
"Sign in to Google to save your progress. Learn more"
If you want to set your mind at rest that your email address will not be saved with the Form (although it definitely won't be), copy and paste the URL into a Private/Incognito window or sign out of Google before completing the Form. 👍