Not my area of expertise, but I'd remove the tile. Bonds can fail, but I'd wager bonding concrete to concrete has a much better chance than concrete to tile. When plaster pools are resurfaced, TFP often recommends a complete chip out of the old plaster for that reason, as opposed to just laying new plaster on to old (which is done, but doesn't make for the best end result). It's on that advice I'm basing my "guess."
I would think in the deepest part, where there will be the thickest layer of added concrete, you'd probably be fine. I'd most worry about where the new layer of concrete tapers to a much thinner layer in the shallow end. How thick do you expect that will be?
There is the bond to consider, but also the current adhesion of the existing tile to the subsurface. It doesn't matter how well the new concrete bonds to the old tile, if the old tile comes loose from the old subsurface.
Chipping out the tile would be a lot less work than having to redo the new bottom if the bond fails. Though I cannot say how much the chances of that changes by removing the tile.
Perhaps
@JamesW can lend his advice.
That all said, I wish my pool was deeper! Not shallower. I would
love an 8' pool. Can we ask why you want to change the depth?
Something else to consider: when I resurfaced my pool, I had them seal up my drains. No more stuck vacs. No more stubbed toes. It looks so much nicer to me without the drains. And of course it eliminates a potential entrapment hazard, and the possibility of any sort of main drain plumbing failure. My pool works fine with one skimmer. If you would consider that, then you might shut off your main drain now, to see how your pool performs without it. If you notice no difference, then get rid of it. If you can't keep the pool as clean or clear, or as well-circulated, then you probably should leave it. Hot/cold temperature spots is a symptom of inadequate circulation.
Some swear by a main drain because it can protect the pump from starving of water if the water level drops below the skimmer mouth. But your skimmer has to be of the type that can close itself off when that happens, or this is basically a non-issue. But it's something to be aware of should you want to remove your main drains.
If you only have one drain, and decide to keep it, now is the time to install a proper two-drain anti-entrapment system. Some cities/states and/or contractors won't allow a remodel without adding that second drain. (Though eliminating drains also satisfies the code.)
There is very little reason to have a drain, as they are rarely used for anything and aren't particularly good at circulating your water (as counter-intuitive as that sounds). They are old-school, and a throwback to when pools were cleaned by manually sweeping gunk into the drain. Modern cleaning vacs and robots now clean pools. And draining is most often, and most safely, does with a small sump pump.
