It can be done on a moderately powerful GPU these days, but only to about 10x zoom (or maybe less, I don't remember) before it starts to look weird. The main problem is floating point precision (or lack thereof) causing distortion :(
Don't you need increasingly high numbers of iterations at higher zooms as well? I don't know if this is an actual property of the render, but I recall it being an issue the last time I programmed it, even with just double precision floats.