That is one possibility. A carpenter would have been a skilled tradesman, building houses, tables, chairs, cabinets, trading his skills for profit. With the title of carpenter, he would not be a mere laborer or a subsistence farmer. If anything, a skilled worker could be a member of the middle class.
Years ago I read the word "carpenter" is mis-translated, and have been searching for something to confirm that. Here is the best I've found:
"Today I found out Jesus wasn’t really a carpenter, at least not as we understand the profession.
"Now obviously eventually Jesus’s chosen profession was of a “Rabbi” or teacher, so in that sense he wasn’t a carpenter regardless of translation. However, in his early years it is supposed from Mark 6:2-3 that he was, like his step-father, a “carpenter” as commonly translated.
"However, the chosen translation from the Greek word “tecton” to mean “carpenter” is a bit of a mis-translation. In fact, “tecton” (in Mark) or “tekton” (in Mathew) is more aptly translated into a word describing a “contractor”; specifically, contracting as a “builder” or “handyman”. Not necessarily having anything to do with wood in most of the jobs he likely took.
"He was basically a “Mr. Fix it”. You had something that needed mended/fixed, designed, or built and he was the guy to call.
"And note, this isn’t just referring to small jobs such as repairing a leaky roof or the like, though this type of thing would have likely been a part of what he did when bigger business was slow; but it also refers to such things as designing and building bridges, stone temples, etc. So perhaps by today’s notion of the profession, he’d more likely be called an “engineer".
Again, I say the question is: which end of the scale were Joseph & Jesus? Were they just some itinerant part-time handy-men, and Jesus a part-time teacher; or were they at the top end of their trade: the more prosperous builder--contractor--engineer?
If the Shroud image is considered authentic, and its height determined as at or "above average" for its time and place, then that suggests a rather prosperous upbringing -- as a minimum, there was steady work and good pay.
Historically speaking, such steady work on large projects was easily there to be had, of course, about an hour's walk from Nazareth, in Sepphoris. My point in all this is: does it make sense to consider Joseph & Jesus to be major contractors for the tetrarch of Galilee & Perea, Harod Antipas?