Yes, an extra dot in the username part of the email address does not change who gets the email address at Gmail.com. Please be careful to notice that this might not be true of all other email service providers.
For example: [email protected] is the same as [email protected] or any variation of the position or number of dots before the @ sign. If someone tries to open a new Gmail account with just a dot as a difference between their address and yours, Google will tell them the username already exists.
Caution: if you used Gmail through an organization like school, business, or company, your dots do matter.
More on this in this Gmail help article.
Have you experienced anything that contradicts the above? Please share here in comment.