Some 4.00" tires will partly fit, that is with the rear wheel at the farthest end of its adjustment, but will not allow the wheel to be adjusted fully forward. The Avon AM26 4.00"x18" being a good example, the actual width of the one I tried on my project bike was more like 4.375".
(Replaced by a 100/90x18). Check the tire manufacturers' web sites for the actual width, 4.00" = 101.6mm.
Some nice features on BW's Asbo custom, there's the basis of a great-looking flat tracker in there.
Regards,
A.