Well yes, but the differences are tiny. Here is an example.
Lets say we have a Cree XHP-35 HI E2 @ 2.5A with a luminance of around 136cd/mm^2 (see luminance test here).
Lets say we want to put it into a Convoy C8, which has a medium-sized reflector (large opening has a diameter of 37.6mm). The light also has an ar-coated lens with 96% transmission (cheapo Chinese lens).
Imagine that we have two different parabolic reflectors (aluminium), both with the same large opening. One has a small opening with 5mm diameter and is deeper and the other has an opening with 10mm diameter (more shallow).
Area of first reflector as seen from hotspot: (37.6mm/2)^2 * pi - (5mm/2)^2 * pi = 1091mm^2
Area of second reflector as seen from hotspot: (37.6mm/2)^2 * pi - (10mm/2)^2 * pi = 1032mm^2
Luminous intensity with reflector 1: 136cd/mm^2 * 1091mm^2 * 0.9 * 0.96 = 128.2kcd
Luminous intensity with reflector 2: 136cd/mm^2 * 1032mm^2 * 0.9 * 0.96 = 121.3kcd
So with such a small reflector there is a measurable difference, but it’s still a small difference.
The thing to understand here is that the effect become less important the larger the reflector is.
Now the same calculation with the BLF GT reflector (118mm). Lets say we have one with a 20mm diameter small hole and one with 10mm.
Area of first reflector as seen from hotspot: (118mm/2)^2 * pi - (10mm/2)^2 * pi = 10,857mm^2
Area of second reflector as seen from hotspot: (118mm/2)^2 * pi - (20mm/2)^2 * pi = 10,622mm^2
Luminous intensity with reflector 1: 136cd/mm^2 * 10857mm^2 * 0.9 * 0.96 = 1,276kcd
Luminous intensity with reflector 2: 136cd/mm^2 * 10622mm^2 * 0.9 * 0.96 = 1,248kcd
So when using such a large reflector there is absolutely no discernable difference. Esepcially when you consider the minmum 10% tolerance of optical measurements.
The deeper reflector will make the light longer though. That is something you will notice.
Before you wonder why these values for the GT are higher compared to measurements which have been done, consider that this calculation assumes a perfectly shaped aluminium reflector with perfect 90% reflectivity with a perfectly positioned LED. It’s very difficult to reach the maximum possible value when building such a large light.