No.
The word *translated *as carpenter is, as Diogenes notes, tekton. And as Dio also notes, tekton means “day labourer”. Jesus and Joseph were not carpenters in the modern or even medieval sense of “artisan that works with wood”. They were carpenters in the sense of “construction worker”.
These were impoverished men who gathered every morning in the village square. Anybody who needed work done would come down to the square and hire them at a negotiated rate. Today they might do 12 hours work for real carpenters and stonemasons assisting in building a house. Tomorrow they might finish that job and have no work for half a day. The following day could see them picking grapes, and the day after that they might be clearing stones from land. In the harvesting and sowing seasons work would have been plentiful and the wages high for the best workers. In winter, times would have been very lean indeed, and it was in winter that most people did their building because labour was cheap.
These men had little need for literacy or numeracy, and less opportunity to learn. They were told what to do by the real tradesmen and businessmen. They were truly unskilled labourers.
The image of Jesus and Joseph as carpenters working with wood is a misconception. While they may well have worked with wood at times, they may also have gone years between doing such jobs. There is a good reason why Jesus’ parables are so full of stories of men doing harvesting work or making mud bricks or similar menial tasks. That is the type of work Jesus would have been most familiar with.
So the idea that Jesus must have been literate and numerate because he was a carpenter has no basis in scripture or history.