Will a circuit tester tell if current is in an auto bulb socket? If you touch both leads
With the probes?

I'm inclined to say no, but first let me make sure I understand your question. If you want to know whether current is flowing, you need to insert an ammeter into the circuit, so that current lows through it. Simply touching the two probes on either side of a light bulb won't tell you whether current is flowing through that bulb. And if the bulb is not in the socket then you have an open circuit and current won't flow anyway. However, you can use a voltmeter to check for the presence of voltage between the two contacts of the lamp socket. You can check that you have a proper 12 volt difference between the two contacts. This is the way to verify that the socket is working.

Yes, there is some confusion here. I think Oneill474 meant to ask if there was voltage in an auto bulb socket... not current. i.e. they probably want to figure out of the bulb is burnt out or if the circuit itself is at fault.

Yes, voltage testers will tell if there is voltage in the socket. Careful with the probes though - you'll blow the fuse if you touch the wrong things.

A multimeter is a much better tool for circuit checks... and they are not that expensive.