Audio EQ - Should all the EQ numbers basically net zero?

No. It doesn't work like that at all.

You might as well turn up the volume knob to gain back the lost amplitude. That will maintain the mix that you just set to your liking. Just set it as you like it.

However, if you do boost the frequencies a lot so the signal starts clipping, then it begins to make sense to adjust the faders in relation to each other until it stops clipping and still have the "shape" that you like, and then use the volume knob afterwards again.

For instance, if you like a lot of bass and turn up the bass, then it'll likely clip. It might be better to turn everything else but the bass down and then boost the volume.

This is mostly an issue for the bass area. Our hearing is (logarithmically) less sensitive to low frequencies, so in order to turn up the bass we have to make it much louder than if we want to turn up the treble. The bass easily takes up the entire "headroom" available in the signal, resulting in clipping before it is amplified. The rule of thumb is that cutting is better than boosting.

Anyway, unless you're compensating for a bad speaker or similar, it's generally best to leave the EQ alone. Professionally produced music is already mastered to utilise the entire frequency spectrum in a balanced way so that it can be safely turned up without having certain frequencies dominate the output or to turn it down without losing the details.

Using an EQ post production is somewhat like salting a gourmet meal. Chances are that it's making it worse unless you know why you're doing it.

Obviously you can listen to music however you want, but please pay attention to what happens when you turn up the volume. It's likely that you'll want to use less EQ as the volume goes up.