To put it shortly: Yes, it’s possible to sublimate on coloured fabric. However, it does have its limitations.
Sublimation printers can only print CYMK, which excludes white ink. Also, sublimation ink does not transfer well on dark materials since it is not truly ink, but a semi-transparent dye. Because of this, the print is generally hard to see against a dark fabric as the colour of the fabric affects how the print looks like in the end. Same idea goes for printing on coloured paper. The lighter the colour of the fabric, the better the print result will be. (This answer can also be found in our FAQ as well as an example of the results).
This works best for graphics that are black-only or printing on fabric that is off-white if you are particular about the colour results.
If you require any further clarifications, we are always here to help!