No. A gift tax return is separate from income tax filing. The form is not available from TurboTax.
https://www.irs.gov/pub/irs-pdf/f709.pdf
"Gift Tax" is somewhat of a misnomer. Even though a gift tax return may be required, very few people ever actually pay federal gift tax. The purpose of the gift tax return is usually only to document a reduction in the allowable estate tax exemption.
See https://turbotax.intuit.com/tax-tools/tax-tips/Tax-Planning-and-Checklists/The-Gift-Tax-Made-Simple/...
