I don't know why I'm replying to this; the thread's nearly six years old and I doubt the OP's going to read this, but anyway
Short answer: No.
Long answer: Both movies judging by the technology, clothing, hairstyles, etc. take place in the '90s. Josiah judging by that B&W photo of him and the ages of the old ladies who tell his story lived and died decades before the '90s. So, unless Josiah used a time machine to travel back to the '30s/'40s, there's no logical way in hell that he could be the baby from COTC V.
If this is a consular ship, where is the ambassador?

But then later they indicate that Josai is the son of one of the ladies.

Nah. If you listen to the old woman's story Josiah came to town with a bunch of traveling preachers. The preachers did everything they could to keep Josiah young (i.e. pouring mercury (quick silver) down his throat to stunt his growth) but Josiah was still growing up so the preachers killed him. Then Josiah came back from the dead and killed the traveling preachers with a harvesting scythe.
It seems the sweet little children of Gatlin have locked the door