You can probably get lots of comments from users of Doppler DF antenna
systems about the performance to be expected. (There's a "fox hunting"
email list that could get you into a group with lots of
direction-finding experience quickly.) Of course, since indicated
direction depends on the detected phase of the received Doppler-derived
FM modulation, relative to the antenna "rotation," it is important to
use a detection path that maintains a very stable phase shift. It's
generally useful in practice to have a very narrow filter on the
Doppler-derived FM, so that other modulation on the signal does not
interfere with your detection. You can do that with switched-capacitor
"analog" filters, or with digital filters, locked to the
antenna-switching subsystem. Expect multipath to mess up your
indication just as it can with any other direction-finding technique.
Many practical factors affect how well your antenna system will work.
Beware of the mutual impedance among all the antenna elements: you
will probably want to insure that elements which are de-selected are
non-resonant. If you don't need very fast indication of bearing, you
may do better with a rotating directional antenna, ESPECIALLY in terms
of minimum detectable signal. If you want to know just how well this
Doppler DF scheme is going to work with a particular signal (with
perhaps broadband complex modulation), I'd suggest that it's a pretty
easy experiment to set up, either with the antenna and receiver you
plan to use, or even by generating a version of the source signal with
FM added. I have this vision of you trying to detect something that
looks like 5MHz wide random noise modulated by a 50kHz-deviation FM,
using a receiver with a 50kHz or 100kHz bandwidth, and perhaps being
very disappointed in performance.

Finally, why didn't you indicate in your original posting that it was a
particular direction-finding application that you were interested in?
That probably would have gotten to the point a bit quicker.

Cheers,
Tom