Can a sink drain into the W/D drain pipe horizontally with a Wye?

[newrenoguy]

I'm renovating my basement and we wanted to add a utility sink to the W/D room.

Would the configuration below work for proper draining or is there a risk of the W/D water filling up the sink? I would be tying in the sink drain with a long Y into the horizontal drain and an Air Admittence valve for venting.

Thank you.