No.
Federal Tax Refunds are safeguarded from being garnished for Student loans until May 1, 2022.
As a side note, this year it is possible for taxpayers to file Married Filing Separately (MFS) and claim the Child Tax Credit, however they may lose other credits compared to filing Married Filing Joint.
Additionally, if the couple live in a Community Property State, they may need to claim half the income of what they would claim on a joint return, thus canceling the advantage of filing separately.