If they are 600mAh batteries then that means they can theoretically supply 600mA for 1 hour. You can't test this by just touching a meter (or any other test gear) on the battery for a sec and taking a reading. There is no way to know how much energy is in the battery other than to discharge it and see how long it takes. ie, connect the battery up to some load, like a light bulb, and record the current readings at regular times until it's flat. Then you can work out what the capacity of the battery was using the current readings and the length of time it took. If the battery was fully charged when you started then you have worked out the maximum energy the battery can hold which is what the 600mAh written on the battery means.
If you just wanted to see how 'good' the battery is then set the meter to volts and take a reading. 1V=flat 1.5V=full or 1.25V=good (if it's a rechargable battery).
Sometimes people do connect *small* batteries up to a meter on the 10A scale for a fraction of a second to see how charged a battery is. However it's a very bad habit as it's not all that good for the battery and if you ever did it to a big battery your meter would probably explode, or at the very least blow the fuse. (even a little AA can supply over 10A if it's a good quality one and fully charged when shorted out)
The readings you get when you do do it are a combination of how much current the battery can supply under extreme and ridiculously high load and the batteries internal resistance. Because the battery is being pretty much shorted out the voltage is so low that the readings are pretty meaningless except to compare with other batteries tested the same way on the same meter. Different meters will give different readings as they're not really designed to measure current at such a low voltage.
So, long story short.... Don't do it, its bad