It is possible but not the most likely outcome, and the specifics of why he is on probation matter more than the probation status itself.
When an inmate is approved for home placement, the supervising agency does not simply rubber-stamp any address submitted. They review the proposed residence and the people living there as part of determining whether the placement is appropriate. A household member on probation is a flag that gets attention, not an automatic disqualifier.
What both probation officers, your daughter's and her father's, will want to know is whether the two supervised individuals living together creates any conflict with either of their supervision conditions. Some probation orders specifically prohibit cohabitation with other people under criminal justice supervision. Others have no such restriction. The nature of the original offenses matters too. If the crimes were unrelated and no indication living together would undermine either person's rehabilitation or supervision, the officers are more likely to find a way to make it work.
The most common scenario in situations like this is that the two probation officers confer directly and make a joint determination. That conversation between officers is actually a good sign because it means both sides are engaging with the question seriously rather than issuing a blanket denial.
The most useful thing the family can do is be transparent with both officers about the living situation before it becomes an issue. Surprises discovered after placement approval is granted create bigger problems than questions raised upfront. If both POs know the full picture and have signed off, the placement is on solid ground.