I have tested 0.031" PCB's with compliant pin connectors in a past life for automotive applications. Performance is very pin, component, and PTH  design dependent. Complaint pin needs the 'compliant' section of the pin to be centered in the PTH. Most CP connectors register against the PCB surface which could reduce the contact area of the pin in the PTH on thin PCB's. Also, the cross section of the PCB will require tighter tolerances on the finished hole diameter to ensure proper retention forces and no damage to the PTH.

We chose not to use CP on PCB's < 0.062" for automotive applications. It might be acceptable for less harsh applications with proper design and part selection.