Can you get lucky with the initial configuration of the cube in some way, or is is shuffled in a way that ensures roughly equally hard solves? What's the protocol here?
Luck can and does play a role. The official regulations for scrambling do require an optimum solution of >x moves. It doesn't take into account solving technique though as that's not really feasible. A scramble might be considered really lucky for a roux solver and unlucky for a cfop solver. It may even be lucky for a cfop solver that builds a white cross but not one that builds a green cross. There are far too many variables to take into account. Especially since one of the biggest sources of luck when using cfop is OLL skips (1/216 chance) and PLL skips (1/72 chance). An OLL+PLL skip would be insane but far too rare for competition. OLL and PLL are the O and P in cfop so occur at the end of the solve so they are pretty much impossible to predict since there are so many possible ways to do the cf (cross and f2l) portions of the solve.
Even if you don't get a skip, some OLLs and PLLs are faster than others. A "u perm" is way better than a "g perm" for PLL. In the OLL step a sune is really fast.
2 is a lot smaller of a number than I remembered but I looked at the regulations in the way back machine and it looks like it's been that way for a while. I kind of wonder why they'd have it at such a low number.
It is possible to get lucky with the original scramble. There are a couple ways to think about it. First, some pieces you care about in the early solve may be in place already (e.g., for a CFOP solve, some cross pieces may be in place), or nearly so. This will save you a move or two.
Secondly, sometimes the combination of the scramble and your early path through the solve creates future opportunities. Sometimes you’re lucky that a later step in the solve can be skipped. With a 10-second inspection time, no one can look this far ahead. With a world record hovering around 3 second, skipping one step that requires a 5-10 moves is a big deal.
The world record for the 2x2 is currently an eye-watering 0.49 seconds. 2x2 solvers use inspection time to plan the entire solve, something not possible with 3x3 and above. So that record 2x2 scramble was solvable in under a dozen moves; that’s good luck.
Even if you don't get a skip, some OLLs and PLLs are faster than others. A "u perm" is way better than a "g perm" for PLL. In the OLL step a sune is really fast.