I measured the latency at around 2-3ms. Whether it's 3ms or 1.7, you're most likely not going to notice it AT ALL. Now, if you add more gear in the chain, like an H9 (3ms), an HX Stomp (3ms), a wireless unit, (3ms), then you'll start to notice it feels a little less 'immediate.' YMMV, of course, but the short answer is that for 99.9999% of people, the native latency in the unit is not bad at all.
That said, the virtual capo (Fractal's poly pitch shifter) still has noticeable latency (30-45ms), but hopefully we'll get the Axe Fx III's improved pitch block which significantly reduces the latency of the Virtual Capo. We may not, though, as it's been on the Axe III slightly longer than the FM3 has been in existence and the FM3 has been in existence for 18 months, give or take. I'm more or less resigned to it NEVER getting the improved pitch block.
So, the unit itself is great in terms of latency, but if you use different tunings and were planning on using the Virtual Capo, you may need to add an additional pedal like the Drop if you want lower latency. All that said, I play in a cover band as the rhythm guitarist and as long as you're not doing anything too intricate, it's fine. It also sounds like trash on clean tones, so watch out for that.