The tri is a chestnut with a broken and two harlequin OR a harli and a non-extension (tort/fawn) genes
Crossing to a self black would give you 50% of broken and 50% full coated chestnuts, and possibly black, tort, fawn, and 100% to 50% will be harliquinized versions of these.
So...yes there's a possibility of getting tris from the pairing? Schweet. I keep resisting getting tris but...they are cute as heck and if I can use my future self black buck for it, I may just break down and get a tri doe. Especially because I'm losing confidence in my BEW program daily.