What emerges from this discussion is that a child can be counted for a minyan in times of great need.
Another relevant point: We find the following in the Gemara (Berachot 47b): “It once happened that Rabbi Elazar entered a synagogue and did not find a minyan present [i.e., only nine men were there]. Thereupon he freed his [Canaanite] slave [who had accompanied him] and included him in the requisite quorum of 10.” The Gemara asks: How could Rabbi Elazar have freed his slave? Didn’t R’ Yehudah say, “Anyone who frees his slave violates a positive command” based on Leviticus 25:46: “l’olam bahem ta’avodu – you shall work with them forever”? The Gemara answers that “for the purpose of fulfilling a mitzvah, it is different.” The Gemara then asks, “But isn’t this is a mitzvah accomplished through violating a sin?” To which the Gemara responds, “A mitzvah on behalf of the larger community [mitzvah d’rabim] is different.”
Now take into account these two practices – counting a minor for a minyan and violating a prohibition by freeing one’s slave to constitute a minyan – and compare them to a Sabbath desecrator who is present in a synagogue. Also remember Rabbi Hodakov’s words, cited earlier, “At that moment, when [the mechallel Shabbat] leads the congregation, is he desecrating Shabbos?” Keeping this in mind, surely there is sufficient reason to allow a mechallel Shabbat to lead the services. We don’t even have to wait for him to reach maturity or free him from slavery to do it!
(To be continued)