I'm sorry but no, she would not. Give your daleel (islamic proof) please.
OK, so I will now start my career as a disbelieving alim (scholar) and will now deliver my own disbeliever's fatwa (religious ruling) :
as far as I know, a Muslim female's marriage to a non-Muslim male would simply be considered invalid (null and void) by most Islamic scholars.
They would say that, by having sexual relations with Chris outside of a lawful marriage, Mary is gravely sinful (she is committing zina, i.e. unlawful intercourse). But in Islam being sinful, even gravely, does not mean that you become automatically a non-Muslim
The problem is different : in Islam, there is (some sort of) consensus over what takes you out of Islam (the so-called "nullifiers of Islam), but zina most surely is not one of them. You could check, as an example
http://www.salafi-dawah.com/things-that-invalidate-islam.html . A more complete explanation here
https://www.kalamullah.com/Books/Explanation of the Nullifiers of Islam.pdfThe issue is therefore more complex, and depends from whether Mary is convinced that, by her sexual relationship outside of a valid marriage, she is going against Shariah or not. If Mary does realise that she is going against Shariah, she is simply a sinful person. Islamically, she should, therefore, sincerely repent, leave Chris as soon as possible etc etc and then it is between Allah and herself.
However, if Mary claims that her marriage and sexual relationship are legitimate in terms of Shariah, she may be considered as going against the 10th nullifier (
Total Disregard or Turning Away from the Religion of Allah (G), by neither Learning It nor Acting upon It). If she considers that for some reason, she is not obliged to follow Shariah, the 9th nullifier could also apply.
So, as I have shown, in Mary's case there is no "automatic" exclusion from the fold of Islam at all. That will be 7 pounds 50, please : via PayPal
And Allah (hopefully) knows
best