I have my encoder connected to the GPS which I believe reduces the satellite search time; it would nice to see the differences (GPS v Encoder)
I think there is a misconception.
The altitude input to an IFR GPS is there for RAIM purposes. The baro input reduces (by 1) the minimum # of satellites required, IIRC. It is fairly meaningless these days.
The altitude info could be used to shorted the initial fix time (by putting a constraint on the PLL) but I don't think this is done on aviation units. It is done in more specialised units; for example a GPS combined with a FOG (as on the U.S. GPS guided bombs) can be made highly jamming-immune because of the INS knowing roughly where it is. Worth reading the Volpe report on GPS vulnerability - online somewhere.
but I believe there is no way that a GPS could give you accurate height information based on a time algorithm.
That is exactly how GPS works! The solution is not just 2D (plan view). It is always a full 3D solution. Due to satellite geometry the vertical portion of the solution is less accurate, but it is still damn accurate. GPS can be and is used by space vehicles.
Interestingly, the principle of GPS (correlation of known-timing packets) was even used on Apollo to get precise space vehicle position information; all those years ago.