It never would have occurred to me to pair these two together, but it makes so much sense!
I love your descriptions of Filch as being like a rough, old tomcat. It's a great touch that Arabella sees him this way, and thus can inherently understand him and see more about him beyond the gruff manner. The attraction here is clearly based on more than simply the squib factor.
"If it were a date, it'd be dress up. And toilet water. And me holdin' out yer chair. Ain't you ever been on a date?" Before Arabella could say 'yes' or 'no' or 'mind your own business', Mr Filch harrumped and slapped the table. "Next Friday. I'll show ye a date."
So Filch! ::dies:: Your characterizations are fantastic and the interaction between them is just a joy to read.