That's an interesting take I hadn't considered. It could certainly seem to follow from 12:38-30 where the scribes are devouring the money of widows.
I wonder if the "treasury" (the place where she is putting money) in vs 41 is connected with temple taxes in 12:13-17? Are these the same funds being used to pay the tribute tax to Rome? It seems they might be... I take the question about taxes to Caesar in 12:13-17 to be Jesus essentially saying not to pay the tax. I wonder if this would go along with condemnation of a system that devours widow's money?
Mark 12:13-17 is referring to the Imperial tax. This was a secular tax independant of Temple taxes. This was the normal taxes subject peoples paid to the Roman state, re-evaluated periodically province by province (the Indiction).
The Temple tax was a separate tax Jews paid to the Jerusalem temple for its upkeep. This did not go to Rome, although Roman governors had been known to seize it on occasion for special works - Pilate for instance, did so to help pay for an aquaduct to Jerusalem, prompting Jewish rioting. The Romans often used Temples as treasuries and took money from them in extremis, so they did not understand Jewish sensibilities that this would be sacrilegious. So the widow's coins are unlikely to go to Rome in most instances.
After the First Revolt, the Romans forced the Jews to pay the Temple Tax to the Romans directly as a punishment - seeing that the Temple had been destroyed. This became the Fiscus Iudaicus, that bred much resentment later.
I don't think I'm the only one, though I would have to find a citation to give more. If I have time later I'll try to find some and post here.
It seems that some who heard him also understood him to be essentially saying not to pay the tribute (Luke 23:2). I think it's fairly easy to conclude this in light of the Law:
Deut 10:14 "Behold, to the LORD your God belong heaven and the highest heavens, the earth and all that is in it.
So in light of the Law, what belongs to God? Everything. So what belongs to Caesar? Nothing. Ok, then give to Caesar what is Caesars -
nothing.
There's also an aspect of having a graven image of Caesar the "divine Augustus" in the temple. Since they have Caesar's image in the temple, he could also be telling his challengers something along the lines of giving Caesar the temple if it's really his or give it to God if it's really God's. I think this understanding is just as radical though as it would look Jesus avoids the question a little and instead ramps up the rhetoric by calling for a revolt. Give God the temple, don't give it to Caesar (seems the funds in the temple would be included).
In any case, the implication was not to pay tribute to Rome.
This would seem to go well with the case that Jesus is condemning a system that devours all the widow has just so they can fork over tribute to Rome.
Interesting. I can see the point you are making. I just need to point out that by the time of Jesus' ministry, the coin probably portrayed the current Caesar - so it would be Tiberius, not the divine Augustus.
The Romans didn't worship Emperors while alive. Tiberius himself rejected the title Augustus on his accession, with its implications of holy otherness, which is why it took much longer for this to become a normal Imperial title (as happened quite quickly for the cognomen Caesar). Augustus was only deified by the senate after his death, as Julius Caesar had been as well. During his life, he did associate himself with the gods in Temples of Roma et Augustus for provincials, muddying the waters a bit - classic Augustus, hiding things in shadows, allowing provincials used to god-kings to worship him surreptitiously without offending Roman sensibilities. He was very shrewd. Caligula and Nero would declare themselves gods while alive, but they were tyrants and megalomaniacs. Claudius allowed a limited worship of himself in Britain along similar lines as Augustus, but this was considered highly scandalous.
Worship of the Genius of the Emperor was common though, a sort of guardian deity/animating principle thing, to which the 'sacrifices to the Emperor' were made, but this is separate to the man himself.
Anyway, so it would be a graven image on the coin, but not a divine one. Perhaps it was an old coin of Augustus, but with currency re-issues this would be unlikely I think.
There is an old story that there were moneychangers in the Temple so that the Temple tax could be paid in a coin without the Emperor on it, to prevent having a divine graven image on the coinage. This is mistaken though, as the Temple tax was paid in the Tyrian Tetradrachm, which portrayed Melqart - an actual other god. It was more likely to do with the higher silver content in the Tyrian Tetradracm than the conventional Roman sestertius. During the Jewish Revolt, this was changed to a Jewish minted Shekel on account of the prohibition of graven images.
For these reasons, I do not think the passage can be connected with Rendering unto Caesar, though I find your interpretation thereof intriguing too. It does go against Jesus telling Pilate his authority is ultimately granted by God as well, so personally I'd still opt for the traditional interpretation thereof.