My understanding is that the GPO would apply to HIM if he was getting Social Security AND his government pension if he had worked in both govt. and private. Or if he was receiving SS spouses benefits from your record of work.
GPO effects spousal benefits. In this case, the husband's spousal benefit will be offset by his government pension. Likely his spousal benefits will be entirely offset.
In this case, the Windfall Elimination Provision (WEP) can reduce any SS benefit he would be entitled to on his own earnings record on which he paid Social Security taxes. But in this case it sounds like he does not have the 40 quarters of earnings needed to qualify for any benefits anyway.
And as Mt2Sea stated, in this the wife's own benefit will not be effected in the slightest by the government pension her husband receives.