Can I use a 1.5V battery tester to read 1.2V rechargeable batteries?

Yes. These types of tester typically put a small load on the battery under test. A rechargable NiCD or NiMH battery will be fully charged at 1.4 volts and discharged at 1.0 volts. A rechargable battery will show a higher voltage with no load than it will actually have under load. Using a regular voltmeter or multimeter in this situation will show a higher voltage than the battery has. Almost any battery will show good with a multimeter or voltmeter.