No, if you file as "Married, Filing separately", your tax refund will not get taken to pay for your wife's unpaid student loans. Offset or seizure of a tax refund only applies to qualified debts of the person filing the return (or persons, if filing jointly).
"Married, Filing Jointly", however, is almost always a more beneficial filing status. If most of the refund on a joint return is attributable to you (not your wife), you can file Form 8379 with your joint tax return.
Form 8379 lets you (the "injured spouse") get back your portion of a jointly-filed refund if it's seized or offset to pay your spouse's debt.
You must file jointly to use this form. Also, filing an 8379 will delay your federal refund by up to 14 weeks.
See the following for more information, especially the link at the bottom of the article (Is it better for a married couple to file jointly or separately?
https://ttlc.intuit.com/replies/3326788
Yes
No
