Corelation between P0.1dB and IIP3
There is a correlation between IIP3 (third-order intercept point) and P1dB (1dB compression point) as shown below.
$$P1dB = IIP_3 - 9.6dB$$

Not exactly. A better way to phrase this relationship would be ...
When a number of simple well-behaved RF amplifiers with little or no feedback and with predominantly third order distortion were tested, the following relationship was found to be roughly true for many of them.
$$P1dB = IIP_3 - 9.6dB$$
If you test systems with schottky diode RF mixers at 'middling' LO drives, and PIN switches, then you get similar figures.
If you test amplifiers or systems with a lot of feedback, or other linearity improving modifications, or at high levels where higher than 3rd order non-linearities are important, or FET mixers, then that relation is not very good.

Is there a correlation between P0.1dB (0.1dB compression point) and IIP3?

Given the sort of caveats above, then yes, but it's not as good a relationship as the above. Less feedback is needed to disrupt that apparent link between compression and IP3, and more prosaically, the 0.1dB compression point is harder to measure than the 1dB point.