It would, provided that the algorithm for finding the surface works will enough at higher iterations.
Generally the problem is that to zoom into 3D fractal objects (accurately) increasing the detail shown proportionately requires say a minimum of time*8 for a doubling of the detail.

OK so I haven't tried it on the hypercomplex version yet but I simplified and improved tthe method and now I'm seriously smug:

http://makinmagic.deviantart.com/art/Improved-Quat-Minibrot-127157826

Cool shape generally, (and nice zoom in), though it does seem almost equivalent to the lathe / 'vase' version of the 2D mandelbrot spun round its own axis... (still, wouldn't mind seeing it raytraced)

OK I now have two algorithms that work pretty well without requiring the derivative. They both work based on the directional iteration density at each step along the viewing ray, one based on the classic "s = u*t + 0.5*a*t^2" and the other loosely based on the Newton step i.e. f()/f'(). The problem with both methods was that a ray passing close to "solid" but missing would then give large values for the calculated step distances just after passing the solid - the solution (as I mentioned above) is to check each new step size against the minimum for the given iteration depth (for that ray) and if it's larger then use the step size for that depth instead, otherwise use the step distance *and* store it as the new minimum for that iteration depth - I also test and conditionally store it for the next 3 higher iteration levels.
Both these methods produce results comparable to full distance estimator and both are between 3.5 and 4 times slower than full DE when used on quaternionic or standard hypercomplex fractals *but* both methods will work when you can't efficiently get the derivative and also for Julibrots and similar formulas where DE has issues in any case. The method solving "s = u*t + 0.5*a*t^2" for t is probably slightly better overall and in that case you have to check for "a" being zero otherwise you get specks (even in the middle of enpty space) - use s=ut instead here However if the main iteration loop of the fractal is slow (e.g. involving transcendentals) then the f()/f'() method will be better since that only requires the single delta value not the double delta i.e. you only have to iterate at step and step + a bit rather than at step, step + a bit and step - a bit.
Note that 3.5 to 4 times slower (on quaternions and standard hypercomplex) than DE is still around 8.5 times faster than my old routine - though just out of interest I'm going to try the iteration depth limitation trick in that routine too and see how much it helps

how do you define the formulas ?
what if i would like to see sin(z^2)+c ?

Errmmm - good luck on that
I guess something *may* be possible ? I don't really know enough math theory.

congratulations,  awesome object! 

On the background there is Buddhabrot fractal. Mandelbrot 3D has also some fog around which transparency is depended on iteration count. For reflections (environment mapping) I used the same bitmap as for background.