If it is in your pocket and you are going thru a body scanner or AIT Millimeter scanner anything in your pocket will cause an alert for additional screening. A wallet would be detected. TSA does not use backscatter or XRay machines anymore, that one did detect a wallet I forgot to take out of my pocket.

If it is the metal detector you could probably get a wallet thru as the metal content wouldn't reach the detection threshold which is set pretty low, my hip sets it off but does not set it off at metal detectors at sports stadiums.

The new infra-red thermal conductivity scanners don't penetrate the clothing but detect changes in temperature from the clothing to objects carried in or under your clothing, don't know if it would detect a wallet that has just been put back in your pocket after showing your ID to TSA.

My experience I have to empty all my pockets including my wallet, I have Pre-Check but I can't use the Xray machine due to metal implants. If I forget something, even a penny it has been detected by the millimeter scanners.