It would've been disastrous for Russia. Napoleon's army didn't live off the land, anyway, but supplied itself from the Baltic Sea after the Emperor's accommodation with Bernadotte. Hence why Napoleon headed straight to St. Petersburg.
Few comments (no offense is intended
):
1st, at least to some degree policy of the scorched earth had been implemented during the Russian retreat.
2nd, while initially Napoleon's army had been carrying with it considerable supplies, they did not last even through the invasion stage and when one is talking about the supplies, don't forget that "the horses do not have patriotism and can't be left starving" so there was a need for foraging on the way. As a result, there were serious losses of the horses due to the inadequate food (especially not fully ripe grain).
3rd, an idea of supplying the Great Army through the Baltic ports would not stay to any serious criticism (sorry). To start with, which "ports"? Then, try to imagine a logistic effort needed for carrying the adequate supplies from one of the Baltic ports in French hands (not Riga or Revel) all the way to Smolensk or Moscow. How many carts (and horses) would it take? Not to mention the trifles like an absence of a significant French naval force on the Baltic Sea and presence of the Russian and British navies there. And, of course, it is an open question what would be a starting point(s) for these supply ships and how the supplies would get there?
4th, almost the last thing Bernadotte wanted was "accommodation" with Nappy even if he was rather reluctant to break relations openly until getting issues settled with Alexander. To start with, they did not like each other (even if Bernadotte was formally a part of the family). Then, for Sweden alliance with Napoleon meant adherence to the Continental System, which Sweden could not afford because Britain was the biggest (and perhaps the only) customer of the Swedish exports. Nappy COULD promise Bernadotte return of Finland but there was no guarantee that he will not take his promise back if this would be a part of his settlement with Alexander (much more important for Napoleon than Bernadotte's interests), besides, the combination would mean that Sweden risks one more war with Russia. In other words, almost as soon as Bernadotte sides with Napoleon, his position in Sweden is jeopardized (and it is not such a big problem to find another crown prince).
5th, in the terms of supplies Sweden, even friendly to France, would be pretty much useless: it could not provide supplies for 400,000 soldiers and it did not have a navy capable of protecting the caravans sailing across the Baltics (to where?).
6th, there seems to be a fundamental confusion about Napoleon and his methods of warfare. He was ALWAYS going for destruction of the enemy's army with (generally correct) assumption that after this goal is achieved, the opponent would ask for peace (did not work in Spain). Move toward St.-Petersburg would be something contrary to that method because it was leaving the Russian armies intact on his extended right flank. Capture of St-Petersburg would solve nothing: Alexander still has his armies (with the numbers growing, in 1812 Russians were still in a process of increasing their military forces) and Nappy has to chase them sooner or later. Only a small portion of the European Russia is lost so there is still a huge space for maneuver. Economically, the lost part is important but not critical and Russia can keep getting the British supplies through the Black Sea ports. As soon as the Great Army starts moving to chase the Russian armies, it starts having the same supply problems as in OTL. So basically, Napoleon is losing a year of campaigning.
