No, you do not. If you received a 1099-G, that will have your Paid Family Leave (PFL) income on it, and thus it will not appear anywhere on your W-2 wages statement from your employer.
They are two separate documents, should be treated separately, and need to be entered into TurboTax separately.
For an example of this, and a more detailed explanation of PFL, please refer to the webpage link directly below, where we answer a similar question to yours, about Paid Family Leave benefit tax treatment in California. If you are asking about another state that offers PFL benefits, then you would treat them similarly to the example demonstrated for California. Here is the link to our other, more detailed, answer:
https://ttlc.intuit.com/questions/3436762
Clarification regarding Paid Family Leave (EDD California).Thank you for asking this question.