UCL also has a similar rule in determine the ranking in group stage.
According to 17.01a, "higher number of points obtained in the group matches played among the teams in question;" which is similar to head to head result.
In 17.01, it does state that the ranking is determined after completion of the group stage. But we still rank them after every single game in group stage, and the ranking is determined by head to head result if they have equal point.
I think Serie A also rank the team in similar way, unless it states clearly in the rule that Goal Difference go before head to head result in mid season, and head to head result only counts until home and away games are played.
From what I have read, the rule of serie A determine ranking if two teams have equal point, head to head result is the first thing we look at. Nothing mention it only kicks in after 2 games are played. Just like UCL rule.
Without a reference, I can also say I remember I read an article on Skysport, Football Italia, EPSN SOCCER, saying that head to head result are always the first thing to look at if points are equal no matter it is mid season or not.