GPS and ground speed

Since

(a) Ground Speed can be determined by GPS,
(b) the relationship between the aircraft's attitude and the angle of
attack should theoretically be unvarying and
(c) the attitude indicator is a gyroscopic instrument,

is it possible to assume with any correctness that during cruise, an
aircraft can only be at *a* particular ground speed at *a* particular
altitude at *a* particular attitude? If the answer is Yes, is it
possible to develop some formula where the pilot can at least arrive
at a rough airspeed figure using the GPS should his pitot tubes get
blocked or iced for whatever reason? I acknowledge that this will only
be a rough estimate since headwind and tailwind can't be measured.

I'm thinking about the recent Air France crash and wondering if at all
it could've been prevented using such a calculation to roughly
estimate the actual airspeed instead of having to rely on entirely
inaccurate IAS...

Thanks in advance for your views,

Ramapriya