It's slightly possible, but IIRC, at the time, communications between Russian Poland and Lithuania with the Baltic at the time were hampered by the fact that there were no proper ports in the region other than Riga, which is, IIRC, already well-garrisoned and a hurdle to capture (and even if it isn't, Russian troops will be marching straight to it to try and recapture such an important position so close to their base of power).
Which just means the peasants will be abandoning the rebellion three months later than IOTL, then.
Except Spain during the Napoleonic Wars was a much different case than Poland is here. It has direct contact with the Atlantic and Mediterranean, seas that can be properly dominated by the Royal Navy and used as lanes for shipping supplies for the resistance, not to mention that the aggressor, France, is also distracted with numerous ventures across Europe that will limit its ability to fight. Poland is pretty much landlocked, surrounded by three great powers hostile to her and willing to ally themselves to keep her from rising up again, which means only a WWI-like destabilizing scenario is enough to give Polish independence any momentum.
Well put but you are missing few more important considerations. In the case of Spain the French were brutal
foreign oppressors who overthrew the legitimate regime, looted the country and tried to introduce the reforms which majority of the population did not want. In 1863 the Russians were there “forever” and while the landowners and educated classes could consider them as the oppressors (rather funny because, for example, Traugutt participated in the Russian intervention in Hungary and then fought as the Russian officer in the CW; did not make an impressive career but this is not too important) for the peasants the oppressors were these “patriots” and Russian administration was not associated with any noticeable cruelty or oppression. On the Ukrainian and Belorussian territories the Russians were actually not foreigners at all.
Then goes demographics: in Lithuania, Belorussia and Ukraine the landowners (oppressors) had been foreigners (Poles) and in the last two cases of a different religion as well (so in Ukraine 75% of the insurgents were landowners and in Belorussia majority of the Orthodox peasantry did not join an uprising). Which leaves mostly Russian-owned part of Poland and part of Lithuania as a potential peasant recruiting area and even with the earlier introduction of the land reform (for implementation of which the insurgent government did not have either apparatus or money) the effect would be easily countered by the Russian government which offered land
without any need to fight. More than that, the peasants were interested in capturing and delivering to the authorities their rebellious owners because they’d get a confiscated land (Stefan Zeromski hardly can be accused in a shortage of Polish patriotism or Polonophobia but he described such cases in his novels). Pretty much the same goes for the general mobilization: the insurgents did not have a necessary administrative apparatus, facilities and cadres for training and weapons to conduct it. Not that they were truly controlling terrotory of Poland and Lithuania to make such a mobilization declaration more than just a piece of paper.
The next thing is that a wide spread of the uprising was to a noticeable degree self-defeating and based upon illusions. Prussian convention with Russia (including permission to use Prussian railroads to transfer the Russian troops) expanded initial scope of the uprising, which was seemingly good for the insurgents. However, when it was a small scale local uprising Austria was relatively sympathetic but when it spreaded the attitude changed to the openly hostile all the way to introduction of a martial law. The insurgents expected uprising to spread to the Russia proper (“for your and our liberty!”) but this did not happen because the Poles, in general, were not popular in Russia and because the emancipation reform was already going on.
As far as Prussia was involved, there was no interest in getting an independent Polish state (French client) as a neighbor and while Bismark was cautious, he considered France as a future opponent while Russia was a historic ally (against France). Britain on her own was not a significant factor in this equation and France had a long way to march to get troops anywhere close to Poland. Massive naval operation was not practical on the Baltic Sea: during the CW, allied operations on the Baltic did not produce any results besides taking a single unfinished isolated fort. In the case we are talking about there would be a need to land few hundred thousand French (and British) troops with all necessary supplies and equipment against strong Russian and Prussian opposition and with the major ports being well protected. Fat chance.
Now, the fantasies aside, France and Britain in 1863 had been talking about amnesty and developing some kind of an autonomy, aka, even less than Poland had before 1830, and their (and Austrian) efforts were strictly diplomatic. Britain wanted to avert the Franco-Prussian war and to prevent Austria-French alliance so little Nappy, even if he became too aggressive, which was quite unlikely, would be on his own.
In a meantime there are still less than 40K ill trained, inadequately armed and disorganized (there were no structures which would make these separated bands into a true army) insurgents against 150 - 200K of a better armed regular army. The odds 5:1 are much worse than Napoleon was facing at Leipzig (2:1) or the French at Sedan.