In the 1918 constitution of the RSFSR, the right to vote (from local soviets all the way up to the federal Congress of Soviets) is specified to be restricted to people 'who have acquired the means of livelihood through labor that is productive and useful to society' and members of the armed forces. A range of groups are explicitly disenfranchised, most notably traditional capitalists, rentiers, clergy, and private middlemen. [1] Broadly this arrangement carried over into the early USSR after 1924.

While some of those latter groups might be considered 'white-collar jobs', the category as a whole isn't mentioned. Usually, in fact, white-collar workers were part and parcel of the project of revolutionary transformation by necessity and were typically identified with the working class in general, even though there were often practical conflicts over resource distribution between white-collar and blue-collar workers. Thus Daniel Orlovsky notes that 'during the 1920s public identification of white-collar workers and their organizations with the proletarian project ... diverted attention from many smaller class and occupational conflicts ... over scarce resources'. [2]

Of course it should be noted that the category of 'white-collar worker' is something rather different in early 20th century Russia to the managerial class that emerged in capitalist countries. Orlovsky's chapter is well worth reading for more information on this topic.

[1] Constitution of the RSFSR, chapter 6, subsection 24, and chapter 13, subsections 64 and 65. (Reproduced here)

[2] 'The Hidden Class: White-Collar Workers in the Soviet 1920s', in Siegelbaum and Suny (eds.), Making Workers Soviet, pp. 220-252, here p. 246.