#57 gravel in place of paver base

Definitely. Be sure to put a layer of heavy-duty landscape/sediment fabric between the 57s and the base. The smaller gradation (size) of the base material would settle into/through the gravel with out a fabric barrier. Be sure to compact it as well, if not, it may settle unevenly which could lead to damage to your hot tub.

I actually had extra #57 in my driveway. I put that down first, but still used paver base. Just used less. It fills in the bigger gaps of the 57. Then tapped that down before leveling sand.

mmmm... no, I personally wouldn't do that. The sand may infiltrate down into the gravel and become uneven. You aren't clear about what you are putting on the sand, if it's pavers to set your hot tub on definitely not, it it's a 3" concrete pad for the hot tub then you could just forget the sand and place the concrete directly on the gravel after leveling the gravel out and consolidating it with a plate vibrator. If you use pavers the idea of the sand is to give you a nice smooth surface to set your pavers on, the base for the sand should be something that can be generally smoothed out, then compacted to help prevent settling. The base has a lot of fines mixed with gravel to achieve the compactability. The surface of the base after compaction is tight and less permeable so the sand sits on it and doesn't filter down or settle which will keep the paver surface nice and even. If you try to use gravel for the base of the pavers I'm afraid that it will be extremely difficult to level the pavers during the installation, plus the sand in the joints between the pavers that helps lock the pavers in place will settle out leading to the pavers coming loose and moving around. Good luck.