The short answer to your question is, technically, no. A private creditor cannot garnish your tax refund. State and federal agencies are the only entities allowed to garnish tax refunds. However, if your refund (the refund is yours because she has no income from which to withhold income) is deposited into a joint checking or savings account, the judgment could be used to garnish the account. As a result the refund could be in jeopardy. The judgment could also be used to place a lien on any property with your wife's name on it.
Even though your wife is now a full-time student and not working, you both will benefit if she addresses this vet debt before she graduates. Many employers perform a credit check as a means of evaluating potential employees. All other things being equal, your wife's poor credit history may cause her to lose out on a possible position to someone who has a good credit history.
I recommend that your wife work out a plan to pay off this credit card debt. I suggest that she consider a part-time job. She could get a double benefit if she found a part-time position in her professional field. If it's not possible for her to work, you could try to cut expenses enough to make a sizable payment on the credit card debt.
Since you expect to get a tax refund, you could allow her to use at least a portion of the tax refund to pay the debt. Her credit report will still show the delinquency and public record of the collection judgment. But in my estimation, from an employer standpoint, the negative impact will be much greater if the debt is still unpaid after being ordered by the court to pay it back.
I have one last concern on how the unpaid debt could affect your wife. Employers are not the only ones who use credit reports and scores as evaluation tools. Insurance companies use them to set rates for their customers, too. That means you could be paying higher premiums for home, auto or renters insurance. So, take my advice and pay this debt as soon as possible.