Unfortunately there is no relation between the pool size and the luck in the direction you want. It's the opposite ...
When the luck increases - more people are joining, but then it should go down to compensate it and it look like the higher hashrate is causing the bad luck, but it is not. If no new miners join the pool a 12h block will actually take 13h
Why 'unfortunately'? Because if it was true, then a solo miner with CPU, would have much more luck and much bigger reward, then no one would need to join a pool at all.
I'm also afraid to tell you that 'luck' does not exist - you can calculate probability but not luck (unless someone could post the calculation for the likelihood of luck existing)...
One certainty is that as the pool grows then so does the traffic into servers and it doesn't matter how much hashing goes on, it has to get to a server and 800-825TH seems to be the current 'lucky' number range.