Does lowering CPU core speed save power?

Most likely, yes. I would like to say absolutely yes, but you can't say that if you don't actually test it. Component temperatures tend to rise as more power is used, and tend to decrease when less power is used. If the temperature also dropped it's pretty much guarantied that your power consumption dropped.

Will the reduced power consumption noticeably affect your electric bill? I doubt it. Greater effect if you turn off the computer whenever you are not using it.

If I remember correctly, power scales directly with core speed, and directly with voltage squared. So, you have saved some power, and if you decrease the voltage as well (it should run at the lower speed with quite a bit less voltage), you'll decrease the power even more.