Is it safe to say that it follows exactly the same rules as FSL GLM (aside from specifying the intercept term)?
Is there a need to demean the covariant columns?
A need: No. It is however good practise; as is rescaling each to unit variance (which helps with preconditioning, particularly if you have explanatiory variables that are at grossly different magnitude scales).
Additionally, if you plan on the direct utilisation of GLM beta coefficient output images, the interpretation of those coefficients may be erroneous if you include covariants that are not demeaned, depending on your model (kind of difficult to demonstrate this concisely, so you might need to trust me…).