The short answer is no. All soviet labor unions were united under ВЦСПС umbrella in 1930s, and this organization was effectively controlled by the state. So, strikes were out of the question, but labor unions were relatively useful for the workers: if you wanted to have a free vacation by the sea, or you wanted to have a free daycare for your kid you could go to your labor union and ask for this (chances of you getting what you want were vary from industry to industry and from factory to factory, but it was not something unthinkable or extremely rare).

So, Soviet labor unions for an average worker were like distributors of free and useful stuff, in some cases they could be useful to solving conflicts at the workplace, but strikes weren’t on the table, because why would you want to have a strike in the USSR, the best country for the working class (it’s not my opinion, I’m just trying to communicate the main idea).

Elaborating a bit more on the post by /u/Lithium2011, I'd like to specify that all of the trade unions operating in USSR were branch-specific unions affiliated with ВЦСПС (Pan-Union Central Council of Trade Unions) that was closely controlled by the Communist Party and thus more an instrument of the government rather that the real trade unions, typical to the capitalist systems. They can be compared to 'factory unions' (sometimes called 'internal unions') that operate within a specific enterprise and are focused on streamlining the workplace by targeting abuse and mismanagement rather than challenging the policy of the employer. In truth, the existence of independent trade unions, along with the right to strike was directly outlawed in the era of War Communism (concurrent with the last stages of the Russian Civil War) and this ruling was upheld by Stalin and remained in place even after the Thaw began.

It should be noted that unlike in the case of capitalist countries, where factories and other production facilities were private property and thus labour disputes were negotiations between organised groups of workers and their employers, in Communist Russia and later USSR, virtually all the industry has been nationalised and thus was the property of the state. This meant that any form of worker's disobedience (strike, lockout etc.) was considered not a harm not the interests of the factory owner, but a direct hampering of the nation's industrial output and thus was qualified as a mutiny or even outright sabotage, especially under Stalin.