Hi,
AFAIK they're nominally about 30 kohms, but with a significant production range and probably will vary with chip temperature, so not really suitable for "precision" measurements. But I believe that they do remain connected to the pin, so your idea should work in principle.
However, the answer really is to breadboard it (and then tell us
) because we have the vagueness of some parts of the base PIC data sheet, and the PICaxe operating system itself, to contend with.
EDIT: The base PIC data sheet (section 30.4, D070 "characterised but not tested") actually defines the Weak Pullup as a current, but it does appear to be moderately proportional to the supply voltage (and nominally 28 - 30 kohms). However, the Min and Max values suggest that the resistance value might be anywhere between 16 kohms and 200 kohms !
Cheers, Alan.