What happens is, if you try to use a current capacity beyond the battery’s capabilities, it might try it but not be up the light spec you wanted, or it may decide not to allow that setting based on voltage drop.

What some high-lumen light companies do is offer a suggestion.
The BLF A6 for instance states (somewhere) that it needs 8 amps to produce its highest setting.
So you would get that battery, if you need that - though it would be expensive.

I do not want to spend the money so my turbo does not activate.
It does not hurt anything, at least in that particular light.
Others might go ahead and run the turbo setting, though it might overheat the battery and shorten its life somewhat.