It would, I've actually been adding those up.
It happened one time in November for an hour, but it was at night and I didn't see it. It happened once in December for a few hours (that was the most we had, I would call it a heavy coating lol), but also at night, but you could see it on cartops and rooftops in the morning and the third time was last weekend and I actually got to see it because it was during the day and I'd call that a light coating.
So three events, one did not accumulate at all, one was a light coating and one was a heavy coating.
The change to rain thing is what I hate because it washes it all away as if it never happened.