There is a Russian saying (it's frequently ascribed to Saltykov-Shchedrin, and sounds to me like something he'd write, but I'm not able to properly source this) to precisely that effect... but not in the way you imagine. Roughly translated, it goes like this - "In Russia, the severity of the laws is compensated by the non-neccesity to obey them".
(I don't have too much time for this, so apologies for shoddy sources down in the answer. Please let me know if you'd like more proper ones, I'll be sure to come back to that later.)
My personal model of Russian corruption maps very well onto Banfield's amoral familism. In a nutshell, the model is that every single individual is morally incentivized to increase utility of his small social ingroup (usually his family, but may be also a group of otherwise associated friends - part of Vladimir Putin's inner circle can be traced back to a housing co-op in the 90s), to the detriment of both his own and society's total utility.
One addition from my own anecdotal experience, that I think Banfield never observed or made, is that an amorally familistic society needs a tyrannical/absolutist ruler to oversee it, lets it collapses into a hobbesian war of all against all - or, at least, that is the usual Russian perspective of it IMO. The tyrant sets the boundaries that make sure the ingroups don't slaughter each other completely in the struggle for utility, and enforces them with terrible, ruthless power. He is, in that sense, elevated from the earthly struggle for utility by that duty - that's why it's not really possible to blame him for any social woes, and instead the blame falls on those that carry out his decisions (and are "earthly" and subject to familism like all others) - there is another, IMO popular, saying to that effect, "the tsar is good, the boyars are bad".
(Ostensibly, this contradicts the saying from the very first paragraph - wasn't it possible to get around draconian laws by corruption? Yes it was. The idea is that while the tsar has his own, directly-controlled enforcers - the oprichnina or the rosgvardiya - and god help you if you cross the law and they notice, he also has a vastly more expansive hierarchy of appointed administrators and law enforcers (whom the average member of society has vastly more chances of encountering in his affairs), who are much more human, hence amorally familistic, hence corruptible.)
Regarding how this maps onto progress, it would probably be useful to consider Acemoglu/Robinson's "Why Nations Fail", keeping in mind two things.
First, Russia is not a progressive country by any means, empirically.
Second, the idea that economic growth equals broadly understood progress is IMO defensible, but not very trivial. But since Acemoglu and Robinson are insititutionalist growth economists, who see technological/scientific progress as the driver of economic growth, it's still not useless.
The WNF take on progress is that people are incentivized to create/adopt disruptive technologies that drive progress only if they have faith in the social/political institutions that will ensure they can extract utility (for themselves, or whomever they care about) from that. If they instead know that institutions care about estabilishing the pre-existing mono/oligopolies, any disruption will be quashed, and progress will be sporadic and unsustainable in the long run.
The Russian case appears to me to be almost that - the ruler is more concerned with maintaining social order than with maintaining the economic status quo (although those two may be connected), but since any large economic entity (like a large corporation running on a technology that is about to get disrupted) is by default more powerful than it's disruptive challenger, it works out the same. The amoral familism begets a ruler concerned with enforcing boundaries and the status quo, and disruption just goes agains the grain of both.
To conclude, yes, corruption does get used as a way out of overregulation, but not neccessarily to the benefit of long term progress.
(Acemoglu and Robinson also make a more direct connection by claiming that you neccessarily need a liberal democracy to estabilish these institutions that are conducive to progress and disruption. I'm hesitant about accepting that head on, but if you choose to agree with that, the case is even easier - amoral familism sees democracy as just ridiculous, and liberalism as weak. If I'm amorally familistic, I only care about satisfying desires of my ingroup - why would I ever want to live in a society which equates my desires to ones from outgroups instead? And if I choose to have a ruler that enforces social order and prevents an all-out collapse, how would he be able to enforce it with terrible punishments if he's limited by some "freedoms"?)
P.S. I have to note that Acemoglu and Robinson are concerned with long-term sustainable growth only. In the short term, however, it would probably be a lot easier for the ruler, or for currently endowed players (like oligopolies/oligarchs) to get things done by getting around red tape.