Yes, this is trivially true once you know that every continuous local martingale is a time-changed brownian motion. Therefore, if you change your time variable $t$ in $dX=a\,dt+b\,dW(t)$ to the right $t^\prime$ you can get a standard tree representation.
Now, the correct time change may be difficult or impossible to figure out, so this theorem is of limited use.
One then becomes tempted to try making a tree adapted to the original SDE. As @lehalle notes, you are then likely to end up with a tree that does not recombine. You may be able to overcome that flaw by interpolating nodes back onto a recombined tree and applying some reasonable boundary conditions, but at that point most people just go with PDE solvers instead.