One needs to ask (as usual!) WHY does she want to do that? What does she think she is accomplishing? If she wants to roll over the gross amount so that there is a larger IRA and no taxable distribution, then WHERE is she going to get the money to pay off the loan? She can't take it from the distribution as that results in the same situation of a smaller rollover. If she has the money outside to pay it off, then why doesn't she pay it off?
NEVER answer a question a client or participant asks (Yes, I said that correctly: NEVER). Instead, always ask WHY are you asking that? Then you will find out the true agenda/issue and probably there is a better way to accomplish what the actual desire is.
All, just, FWIW.
As to your actual question (her question, which is probably the wrong question anyway....), the old chestnut of What does your plan (or loan policy) say? If it says it is offset at distribution, then NO, she can't write the check AFTER distribution. Did you review the plan provisions?