Do high quantity submitters receive better grades?

When submitting to Beckett and PSA? I've been out of the hobby for 5-10 years and thinking about submitting some cards for grades. The business side of me says that those spending thousands to get cards graded will get better "service" than those who submit 1-2 cards. Am I off base?
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There are likely 500 threads on this including one just the other day.
Raw: Tony Gonzalez (low #'d cards, and especially 1/1's) and Steve Young.