[Afton]

It's not right. There are linguistic restrictions on gender-neutral, singular 'they'.[1] When the referent is known, it can't be used (i.e. it's not about 'patrick' and 'he' matching up, it's about 'they' not being usable with a known person).[2]

My favourite real-life example of it's usage is one in which we know that the gender is female, and we know it's singular:

"If a mother wants to use the nursing room, they can just key in the code in their pamphlet".

[1] https://www.reddit.com/r/linguistics/comments/3cgbyv/limitat... gives some good discussion

[2] I can't help but feel that these restrictions are related to nondefinite contexts for "(negative polarity items)[https://en.wikipedia.org/wiki/Polarity_item]", like 'no-one' and 'any', where you can't say e.g.

    *I ate any cake

but you can say:

    I didn't eat any cake

but you can also use it in questions:

    Did you eat any cake?

This seems related to usages like

    If someone comes, tell them to wait

vs

    *If John comes, tell them to wait.