Yes. The note value at which it kicks in depends on the other spacing settings.
With the default space for quarter notes and the default spacing ratio, the spacing of 16ths would be 2.0 spaces, 32nds 1.41, and 64ths 1.0, but the 32nds and 64ths (and anything shorter) are all increased to 1.6 (1 3/5).
That makes 32nds a bit tighter spaced that 16ths, but with a ratio of 1.25 (2/1.6) instead of the default 1.41 for longer notes. Everything shorter than 32nds is spaced the same as 32nds.
If you make the quarter note spacing smaller, the “minimum space” will kick in for 16th notes when they reach 1.6 spaces as well.
If you left quarter notes at 4 and increased the minimum space to 2, that would also make 16ths and anything smaller have the same spacing of 2.