I don't think that's possible, i believe c+m+y will give you a dark brown, but not black, and depending on the colors of the full image it can look weird some times.
and in the design software you will have to avoid using black, and instead you have to use this combination or c+m+y for all the black parts of the image, and if you need a gray color it will be c+m+y with less saturation so it will look just brown, or light brown, and i can't imagine how will you do a dark red for example, or a dark green, or fades to dark colors or black...
i don't know, looks like a lot of impossible situations, at least for me. but if you can solve all that then it would be interesting. you can try it with any regular printer since you already have c+m+y+ in any of them.
but if you cant get decent images with out using black then i believe your option for a dtg with this printer is make it a cmyk only.
hope it helps