In Round 3, 6 ties were selected for live coverage: Friday and Monday x 1, and Saturday and Sunday x 2.
In Round 4 there were 6 ties selected again but broadcast on Friday x 1, Sat x 2, and Sunday x 3.
I don't think it's certain that our tie will get televised. It's a good tie, but then many of them are potential giant-killers with Premiership clubs away from home. Huddersfield play on the Tuesday night so I doubt they'd be too keen on a Friday, but I think City would really like to play on the Friday night. Arsenal play before the FA Cup tie, so they are going to prefer the late slots.
If it is televised, I'd say Saturday is most likely.
Blackburn managed to put out a message almost straight away that they would be playing on Sunday so it sounds to me like a decision had already been made. How could they announce the KO would be on Sunday, unless it had been agreed by the FA, and surely they couldn't do that unless the KO for all the ties had been resolved. But then they do what they want without much regard for the consequences for the football clubs.