Joe: can't tell for sure, since I'm no expert in linguistics (maybe that old crook Chomsky could tell us? Yeah, I know, bad example).
Judging on my personal experience, I would say that "grenouiller" is kind of obsolescent these days. Most people would probably rather use "magouiller" as far as politics is concerned. So the word does exist, and probably has been for quite some time (French political dynasties have a long history of corruption and "grenouillage".)
"manger la grenouille" or even his more familiar variant "bouffer la grenouille" (chow down the frog) is, on the other hand very common and I frequently hear people using it when they start talking about new businesses magically starting with no apparent concern for commercial viability or even well known specialists in frog chow down. Basically somebody who starts a business under his name, gets the subsidies, eat the frog, starts another business under his wife's/husband's name, get the cash, eat the frog, starts another one under his brother in law's name, get the cash, ... well, you've got the point.
And when the family isn't enough, one can still find "associates".
Sure, anywhere else but here, you would call him an unlucky "“ or particularly incompetent "“ businessman/woman. But here, it's just an expert in living on the incoherence of state interventionism.
Meanwhile, of course, no wealth and no serious employment are really created and that's actually the serious problem. Subsidies are wasted, and the creditors of such vaporous businesses usually lost their due since, of course, in such situation the state will serve itself (social assessments and various taxes) on what's left of the phantom businesses.
Sometimes those creditors, if they happen to be already a bit fragile, can even go bankrupt in the aftermath.
That said, the civil servants have quite a similar game: consuming their entire allocated budget for a given year, if possible before the year is over so they will not only make sure that they'll get the same amount the following year, but possibly have a "good" reason to ask for more. Usually, it works quite well. Look closely at what's going to happen in September.