Not completely. ALL equalizers introduce latency – your use of the term “zero latency” is a misnomer. The difference is a linear-phase equalizer introduces latency is that is independent of frequency, that is to say, all frequencies that are passing through the filter are delayed by the same amount, so as a result there are no phase-related issues in the resulting signal. A minimum phase filter, however, introduces latency that is frequency-dependent, so only a certain band of frequencies will be time-delayed.
Both types have their uses. Sometimes it depends on the frequencies you’re altering – a minimum phase filter might sound better on low frequencies. A linear phase EQ introduces both pre- and post-ringing, which in some cases can be unpleasant. Also, if the processed signal is going to be mixed back in with the original signal to any degree, linear phase EQ can sound pretty bad (or good) because the entire processed signal will be out-of-phase with the unaffected signal.
In the old days, before digital linear-phase EQ’s were in use, most stuff was EQ’d “on the way in” in order to minimize some of these issues. On some of my old tapes I can hear some phase issues when I tried to do some fairly steep EQing when mixing through an analog board… not that it necessarily sounded bad, mind you