Question about A7iii / continuous af / lenses

[MMTokyo]

Hi, this is my first post.

I'm seriously considering getting an A7iii, as from what I've read this iteration is where Sony got it pretty close to perfect. I've played with it in stores, and it's seriously impressive stuff.

There's a second hand one in a store here with the kit lens (the 24-70 3.5-5.6) for not much more than most places are selling the body alone. I would definitely be picking up other lenses (a good prime and maybe the 70-200 f4) over time, but my question is this : 

To what extent does the lens impact the performance of continuous AF, and eye AF in particular? When I've played around with it in the major electronics stores here, it has had the G prime 24-70 (where the autofocus was absolute lightning and continuous / eye AF was supernaturally accurate) and the 24-105 (which wasn't much slower, or so it felt). However, am I going to see a noticeable downgrade in performance with the kit lens? It's not like I'm a full time sports shooter or anything, but I can really see an increase in creative possibilities with this kind of AF performance.

If I don't like the kit lens I can always sell it or part-trade it in for a superior lens anyway, but I figured it's worth asking people who may have used it.

Thanks in advance for any and all advice.