Even if the company decides it needs someone to work in the position that homeschooling parent left empty, since most homeschoolers I have known have the arrangement of the man providing for the family while the woman stays home, it would, according to your model, actually increase the amount the person makes as the husband would be required to seek out higher paying jobs (and their attendant responsibilities) to make up for the lost income, thus increasing production, thus increasing GDP.
In addition to this is all the studies which show that homeschooled children contribute more to society than those who are publicly schooled. They seem to be (on the whole) more respectful of others boundaries and less aggressive in general without being passive. This, in addition to having an education at least equal with those from a public school. (Note: the studies which show this are the first of their kind since only recently have enough students been homeschooled to perform a valid study.)
Just my thoughts on the topic.
And many people are currently unemployed. Homeschooling would take other families off the public tit by opening jobs for them.
Your scenario is possible but not likely. Why would the husband already not have maximized his income?
Those studies comparing student populations are gravely flawed by the great differences in the populations studied. If you were to compare homeschooled kids to their social peers (intact families, few extremely poor, not surrounded by social misfits and criminals, the results would not look so favorable as when they are compared to a population weighed down by the children of life's losers. Children surrounded by criminal activity, dropouts, negligent parents etc.)
I am all for truly valid studies being made but those which are biased in favor of one group because of improper modeling techniques are not of much value.