Can a sperm donor later apply for parenting time if there is no written agreement in place?

Potentially, yes — and this is one of the biggest risks of donor conception arranged without paperwork. If there is no written agreement made before conception stating that the donor does not intend to be a parent, a known sperm donor may be found to be a legal parent, particularly where he has had an ongoing relationship with the recipient parent or involvement in the child's life. Once someone is recognized as a legal parent, they generally have standing to seek parenting time and to be involved in decisions about the child, the same as any other parent would.

Whether an application would succeed still depends on the best-interests-of-the-child test a court applies to any parenting dispute, but the more fundamental issue is that without a qualifying written agreement, the donor isn't clearly excluded from parent status in the first place. This is why a written, pre-conception agreement matters as much to the recipient parent as to the donor: it is what is meant to prevent this exact situation from arising later.