Yes
So lets see if I have this right.
1 - She is either a Jew or not. No half way on this.
2 - If she is not a Jew then what she does over Shabbos doesn't matter.
3 - If she is a Jew then no matter what she did over Shabbos does not change the fact she is a Jew.
So all this about what she did or didn't do over Shabbos is a smokescreen. This is really about if you accept her conversion as legit.