You might be right, but my guess is that 7's reputation for luck isn't famous enough to make a difference, and in fact it's common because other numbers seem too "unrandom".
We could test by asking people to pick numbers less than 100. I bet people would focus on odd numbers, especially those greater than 50, not ending in 5 or not having both digits the same.
I definitely overpaid on Mechanical Turk per response, given how lightning quickly the data came in. (I decided to pay $0.10/HIT for 50 responses and got 68 responses in 8m26s.) I suspect that offering a nickel would have gotten the survey filled in under half an hour still...
We could test by asking people to pick numbers less than 100. I bet people would focus on odd numbers, especially those greater than 50, not ending in 5 or not having both digits the same.