TurboTax never knows about offsets to your refund for debts you owed.
NOTE: You can contact the IRS Treasury Offset Program Call Center at 1-800-304-3107 to ask if they have an offset for you on file. TurboTax would not have that information.
No. TurboTax cannot garnish your refund. The article Who Can Garnish an Income Tax Refund? explains who could garnish the refund.
For more resources:
IRS Topic No. 203 explains why a refund could be reduced.
The Treasury Offset Program and Debt Management Services handle student loan offsets. For Federal Student Loan matters, Debt Management Services can be reached at 1-800-621-3115 Monday-Friday 8 am - 10 pm EST, Saturday 8 am - 7 pm EST
[Edited 1/31/2020 | 7:36 am PST]
@KathrynG3 User asked if Turbotax will know about offsets for delinquent student loan payments.