My guess is probably not. I've read that very large coaches with 2 baths may have the a BR sink plumbed into the black tank. But with your floor plan, your sink is most likely part of the gray water system, just like your shower pan.
Definitely speaking, run the sink while the gray tank is shut and see.
2017 Keystone Bullet 308BHS in Saddle.
2017 RAM 2500 Laramie Mega Cab 4x4 Hemi 6.4L
2008 GMC Yukon XL Denali (SOLD)
Hensley SwiftArrow Control Hitch with 1000 lb Spring Bars
Me, DW, (3) little DS's, and 1 rambunctious Boston Terrier