You can have any kind of insurance you want, the question is, can someone make tax-deductible contributions to an HSA?
Your spouse may make tax deductible contributions to an HSA if she is enrolled in an HSA-eligible plan AND has no "other medical coverage." If your PPO plan provides secondary coverage for your spouse, that would be other coverage that would disqualify her HSA contributions. Or, if you enrolled in an FSA, that would disqualify her since an FSA can be used to pay for medical care for the owner, their spouse or their children, even if the spouse and children are not enrolled in the same plan. So you having an FSA would disqualify her HSA contributions.
However, just that fact that you have non-qualifying insurance does not disqualify her HSA contributions as long as nothing you have can be used to pay her medical expenses that might be considered disqualifying.