Not on its own. Mold needs liquid water and food, and closed-cell foam adhered correctly leaves no gap for water to collect and no path for humid air to reach a cold surface. It grows when foam is applied over wet material or specified too thin.
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Mold needs three things: an organic food source, oxygen, and sustained moisture. Wood sheathing supplies the first, air supplies the second, and the entire question is whether the assembly delivers the third. What a correct install does. Closed-cell foam bonds directly to the substrate with no air gap, is a vapor retarder at typical thicknesses, and does not absorb water. Humid interior air cannot reach the cold sheathing because the foam is both the air barrier and the insulation, and the sheathing stays above the dew point because the foam is thick enough to keep it there. No condensation, no liquid water, no growth. The three ways it goes wrong, all of them upstream of the material. Application over wet substrate. Sheathing with elevated moisture content gets sealed in and cannot dry in either direction. This is why a moisture reading before spraying is part of a correct process and not an extra. Insufficient thickness. The foam has to be thick enough to hold the sheathing above the dew point through the coldest part of the year. In Climate Zone 5A that is a calculation against local design temperatures, not a default number carried over from a warmer market. Too thin and the interior face of the sheathing spends the winter below dew point with moisture arriving through any imperfection. Open-cell against a roof deck without vapor control. Open-cell is vapor permeable by design, which is useful in some assemblies and is the wrong choice directly against a cold deck in this climate without a vapor retarder above or a demonstrated drying path. What to ask for: the moisture reading before application, the specified thickness with the dew point basis, and confirmation that the roof was sound first. All three are reasonable, and a crew that has the answers ready is the crew you want.