Can a parent's compliance with a society safety plan affect the outcome of their parenting case?

Yes. A parent's compliance, or lack of it, with a safety plan put in place by a children's aid society can become relevant evidence in a parenting case, because it speaks directly to the best-interests factors a family court considers - particularly a parent's ability and willingness to address a safety concern and to safely care for the child going forward. A parent who has followed through on a safety plan, attended recommended programs, and cooperated with the society generally presents a stronger case for maintaining or restoring parenting time than one who hasn't engaged with it at all.

That doesn't mean compliance alone guarantees a particular outcome, or that non-compliance automatically dooms a parent's case - the family court will still look at the underlying concern, how serious it was, and the overall picture, not just a checklist of whether a plan was followed. A safety plan is also not itself a family court order, so failing to strictly follow every detail isn't treated the same as breaching a court order, though it can still be used as evidence of a parent's approach to the concern. If you're working through a safety plan, keep your own records of what you've completed, since that documentation can be useful later in the family case.