No, that function (GracePeriodDaysRemaining) doesn't do what you think it does. It has nothing to do with IsGenuineEx(). It's (sort of) a precursor to the IsGenuineEx() function (but not really). GracePeriodDaysRemaining() doesn't even exist anymore with TurboActivate 4.0 -- we've completely removed it. It's a confusing and ultimately pointless function that should have never been included in TurboActivate in the first place.
Short answer: that function isn't what you're looking for.
With TA 3.x there's no way to get the IsGenuineEx() grace days remaining or the days until the next check.
With TA 4.x (and newer) the way to get the TA_IsGenuineEx() grace days remaining or the days until the next check is to use TA_GenuineDays().