GT will only make an appearance in one year of all of next gen if they keep up their current nonsense so if Forza keeps up wiith their yearly releases then yh... they should take at least another 3/4 awards next gen.
I honestly don't think Sony cares. GT isn't going anywhere and Forza winning awards doesn't really impact their bottom line. The series did for them what it needed to, and with a new, proper, release (GT7/8/whatever), they will probably get things back on track. It is a massive brand and they need to abandon much of what went wrong with Sport.
With their new push on 1st Party content, I wouldn't even eliminate the possibility of a new racing property altogether, but considering they just took home the biggest GOTY award around, again, I don't think they're losing sleep over Forza winning best racing game in a year where they didn't even release one.