OK, my results using 18X and 5.01v supply.
First off, I tried rev 8.1 and 8.6 firmware. The results (predictably) were very different as 8.1 is pre the 750mS wait. I'll only give the results for 8.6
The code was run on an AXE110 with DS18B20 on input 7 with 4k7 pullup and AXE033 on output 6 all done at ambient of 24.6C.
Connections:
DS18B20 0v to 0v, data to input 7 with 4k7 pullup.
Schottky diode between data and DS18B20 Vcc (blunt end to data), cap between DS18B20 power pins.
The code:
Main:
pulsout 3,150 'blip bi-colour LED each time
readtemp12 7,w0
serout 6,N2400,(254,128,#w0," "
pause 1000
goto main
The results:
Control, Vcc @ 5v, cap=0uF reading=394.
The 5v was then removed and various cap values tested. Temperature kept constant.
a)cap=0uF,reading=498 (and sometimes erratic)
b)cap=10uF,reading=501 (31.3C) (first stable value)
c)cap=220uF, reading=380 (23.75C)
d)cap=680uF, reading=386 (24.13C)
e)cap=2200uF, reading=388 (24.25C) (took several iterations to get up to voltage)
f)cap=6800uF, reading=390 (24.38C)
g) 5v replaced, reading=392 (24.5)
Conclusion:-
Running a DS18B20 on two wires is possible but only with a large cap of at least 10,000uF and under the understanding that the LSB of the 12-bit value will be compramised.
Further testing suggested that the variation in values was in part as a result of the reduced Vcc value. The higher values when C was less than 10uF are almost certainly erroneous reads and bit errors.
To be honest, I conclude that it is NOT reliably possibly with a PICAXE if you require the full resolution. Those of you who use an output pin for Vcc in power saving circuits, take note of the effects of dropped voltage on Vcc when used in 12-bit mode!