It is better to have the hair uncovered and kept in a modest fashion than to wear a glamorous and thus immodest wig. Ideally a woman’s head should be covered with a modest head-covering that does not look like hair. In a society where for whatever reason that will not be done, there is halachik basis for permitting the head to be uncovered with the hair kept in a modest fashion. There is no halachik basis for wearing a fancy wig. As many of my friends here know, I do not hold of the modern-orthodox religion at all. But those who consider themselves ‘frum’ and wear a fancy wig are transgressing ‘das moshe’ and ‘das yehudis’ and they can be divorced without a kesuba if their husband is makpid.
As for the giyoress issue, since as stated, there is halachik basis for having the head uncovered, it is a good gairus if she is not intending to violate halacha. BTW the reason why balei tshuva and geirim may have a problem with head-covering is because they see a contradiction in the fact that she can wear a fancy wig but cannot leave hair uncovered. That’s exactly right. It is a contradiction. Either cover the hair in a modest fashion with something that does not resemble hair (this is ideal), or leave the hair uncovered in a modest fashion. The objective is tzenius, not the wig.