grammar - Can "a person" be considered a collective noun

If used in the sentence:

"Once a person has become X their psychological state becomes Y."

does the "a person" count as a class and thus make the use of the plural "their" correct?

Answer

Once a person has become X their psychological state becomes Y.

No, "a person" cannot be considered a collective noun. In this example, their is a singular pronoun that refers to the "person" whose gender is unspecified. The meaning of the sentence would remain intact if you replaced their with his/her thus:

Once a person has become X his/her psychological state becomes Y.

While this usage of the plural pronoun in the singular sense has been around for a very long time, it was also common not too long ago to use only the male pronoun. In this age, though, one would be considered sexist if one left out the female pronoun. It is also not uncommon to see the female pronoun used exclusively. However, we are all fond of the plural pronoun because it takes care of both sexes and invites no claims of gender bias.

Regardless of what is considered acceptable in various situations, one will definitely come across the usage of plural pronouns in the singular sense when the sex of the person being referred to is not specified.