"They is having a great time."
It does sound wrong for some uses of he/she.
It does sound wrong for some uses of he/she.
The accord with the verb is still as if it's a plural pronoun. Just like with "you" which technically also used to be plural, doesn't take the old singular second person forms: "you have" not "you hast"
“I’m worried about my kid at summer camp”
“Don’t worry, I’m sure they are having a great time”
Sounds very natural to my west coast ears.