By almost any definition, no.

The basic problem was public debt. The War had heavily indebted all the states. Much of the debt was to foreign creditors, and Massachusetts perhaps was the biggest debtor. The merchants of Boston, in control of the government, could not really transact business without any foreign credit, and wanted to put taxes towards paying those debts. Their problem was that hard currency was quite scarce- there was a lot of Continental currency and other promissory notes, but not much in the way of pounds sterling, Spanish dollars, minted coins that had intrinsic value. Shays was one of a number of farmers- landowners, not laborers- who had managed to side-step much of the lack of hard currency by keeping accounts and exchanging personal notes. The new law required them to find enough hard currency to pay their property taxes. Faced with trying to find enough hard currency or losing their farms at public auction, Shays and his followers revolted. That revolt was disorganized ( some of it only consisted of angry farmers interrupting sessions of county courts) and the response was similarly disorganized. The militia raised to put down the revolt made a show of force, the rebels broke up, most (not Shays) were pardoned. The government backed off, legislators who'd proposed the tax failed to be re-elected in the following election.

There were other aspects to the revolt than the debt crisis. Many of the rebels were men who'd recently fought in the War and had been paid for their service with Continental notes, and no one, certainly not the Continental Congress, was redeeming those with hard currency in 1786. The farmers were also from the western area of the state, and there was a real division, existing before the War, between the eastern coastal areas and the less-populated and poorer western, especially the frontier. The eastern regions controlled the government and often ( as in Shays' case) ran the colonies for their own benefit: the Boston merchants' use of the tax system was just one more example. This same division would surface in the Whiskey Rebellion, which was caused by an excise tax imposed by eastern elites that was more costly for westerners.

But it's really hard to find in this any communist revolution. Shays' and his rebels didn't want property distribution, demand land reform. They were, if anything , kulaks clinging tightly to their own farms. There was no rentier class, no landlords wielding an iron fist against their tenant farmers. However, the War for Independence is rather remarkable for how un-revolutionary it was: the same elites who dominated the colonial governments before the War dominated the waging of it, and kept control afterwards. Power did not trickle down to the common people, and some in that governing elite ( like George Washington) were quite concerned about a revolt from below, and "mob rule". He and others saw in Shays' Rebellion the possibility of many veterans ( who knew how to use muskets) turning into that angry mob. But it just didn't happen.