Yes. Anchor bolts get their holding power in concrete by transferring forces through a stress cone:
You want that anchor bolt to bite solidly into the bottom of the slab, to the manufacturer's specification so that cone is appropriately sized. If the bolt is not all the way in, then the cone shorter, where there is significantly less area in the cone to spread out forces. If the bolt is too far in and doesn't bite into the concrete properly, then the cone may not work properly.
There's no reason to sweat this if you have the full 4". An extra inch doesn't do anything for you, strength-wise, because the cone is above the bolt. I think the best practice I see most people take is to get their lift and then take a step back and pour a repar pad (it's not technically a "footer") if they drill for the lift and find the slab is too shallow.
The repair slabs need to be pinned and/or keyed into the original thin slab so they behave structurally as a unit.
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As the lift wants to "tip", with a raised load, the keyed slab will hook into the broader thin slab and help resist that tipping/bending force.