Brain dump regarding using the probe as the only probe.
In theory it would be possible to use the probe as the only sensing equipment as it includes the only variable you need. which is an amplitude reading from the probe (which is then converted to distance)
The issue is there is no datum point, as depending on the scanned surface material, the activation distance could vary.
HOWEVER, assuming there is no minimum distance to the sensing coils, you could put the probe directly against the print surface and take a measurement to create a "zero" reference measurement and store that for later use.
In reality you may want to take various zero point measurements at different coil temperatures and create a look up table of sensitivity vs temperature.
Then once the coils are mounted you would need to set a single Z-offset and that should be good enough.
There is another way off the top of my head, but I cannot remember the algorithms name where you can repeatedly move a reference plate (in this case the bed) up and down a known amount (say 1mm and 2mm) and then you can work out the differences in measurements to gain a pretty accurate depth to probe value. The math was complex the last time I checked, but once I find the name of it, ill post it here as it may be helpful.