It would depend! There are a couple things to look at when understanding literacy; one, in the 1920s and 1930s the Soviet Union aggressively campaigned against illiteracy. By 1917, less than half of men and around a tenth of women were literate [1]; this is only after liberalizing campaigns under the rule of Nicholas II. Ostensibly all Russian soldiers were literate, but this was not really true in practice. The social historian Elise Wirtschafter [2] notes that

"the attainment of literacy by the mass of soldiers was less important to the government than artisanal skills...[but] noncommissioned officers needed to be literate" (64)

and

"[after the Crimean war]...several contemporary commentators noted that many soldiers read mechanically without really understanding the text" (173)

In fact, by 1881, "the army high command lost interest in educating soldiers, and many officers...[thought] that education was positively harmful...the mass of peasant soldiers left the army no more literate than they had entered it." (566) [3]

The likbez program under Lenin and later Stalin sought to achieve 100% literacy. While language policy of the Soviet Union is proposed by Grenoble as pragmatic, nationalist, or legitimizing, it is clear that Russian is the preferred language of the Soviet Union to the suppression of other languages. A census was conducted in 1939, but we will set that aside for now and focus on the 1937 census. The question of the efficacy of these initiatives is certainly relevant (see here) as is nationality; Russians represent 94 million, Ukrainians 26 (down from 31), Belarusians 5 million, Uzbeks 4.5 million, and so on. While they may not be able to read these languages, they could speak them.

The 1939 census was established for, among other reasons, the purported failures of the 1937 census to capture heavily publicized projected growth rates in the 1930s that failed to materialize. In particular, the census would capture the impact of the famine of 1932-1933, and was suppressed [4].

But returning to the question of foreign language literacy for a soldier in 1939, many ethnically Russian soldiers wouldn’t have been particularly literate. Those that were most likely fluent in only Russian, and may or not have been able to read the Latin script; however, a decent portion were not ethnic Russians, such as the Ukrainians and Belorussians mentioned above (up to 25% [5]). Certainly some could read Latin, and others would have been able to speak Polish, German, or English. Isaac Babel’s Red Cavalry gives some insight to language in the Polish-Soviet War.

There is more literature on post-Stalin language policy that may be of interest. In the 1960s, E. Glyn Lewis, who would later write a comprehensive study of languages in the USSR, noted that “until fairly recently the amount of time given to the foreign language was inadequate by any standard and its distribution unsatisfactory” [6]. This is corroborated by our pre-war sources, and helps us understand the post-Stalin shift in language policy. Garrard finds the same, and that "new approaches [and] reforms" were implemented following the death of Stalin [7]. He continues that "few Russians could speak foreign languages...the purpose of language courses in school was seen to be the production of qualified translators” (we can see an example of this is Natalia Baranskaya’s A Week Like Any Other). Abell describes the manner of education not dissimilar to American education, with English, French, and German being offered in middle school, but this particular structure only arises after the death of Stalin [8].

Another factor is the education campaigns of more marginal regions, where there either existed no standardized written or literary form. Latin script was commonly used here, as Grenoble notes, because of political neutrality and practicality when it comes to printing. Regional resistance to Russification tied with Tsarist imperialism allow for

the use of the Latin alphabet [to] be seen as a manifestation of Stalin’s creed of “nationalist in form, socialist in content.” (50)

This policy ultimately was reverted to Cyrillization for rather arcane reasons, as are many of the policy objectives of Stalin. At the onset of WWII foreign languages were taught, but the degree to which students were fluent is unclear. Many soldiers even in 1939 probably read much like those that Grenoble mentions of the late 19th century: mechanically. Nonetheless, certainly some soldiers could read and even converse in Polish.

References

[1] Grenoble, Lenore. Language policy in the Soviet Union. Springer, 2003.

[2] Wirtschafter, Elise Kimerling. From Serf to Russian Soldier. Princeton University Press, 1990.

[3] Bushnell, John. "Peasants in Uniform: The Tsarist Army as a Peasant Society." Journal of Social History 13, no. 4 (1980): 565-76. [4] Merridale, Catherine. "The 1937 Census and the Limits of Stalinist Rule." The Historical Journal 39, no. 1 (1996): 225-40.

[5] Glantz, David M. Colossus Reborn: The Red Army at War: 1941-1943. University Press of Kansas, 2005.

[6] Glyn Lewis, E. "Foreign and second language teaching in the USSR." The British Council. ETIC (1962).

[7] Garrard, J. G. "The teaching of foreign languages in the Soviet Union." The Modern Language Journal 46, no. 2 (1962): 71-74.

[8] Abell, Marcelle Achard. "Foreign language teaching in the USSR." The Modern Language Journal 43, no. 2 (1959): 72-78.

Latin would likely be familiar to many of the soldiers. Foreign languages were taught in Soviet schools, though that of course would vary on school (the famous Moscow Model School No. 25, where Stalin's children attended for some time in the 1930s, had English, German and I believe French classes).

As well early Bolshevik literacy campaigns were heavily slanted towards Latinization. Many of the languages in the Russian Empire/Soviet Union had no literary tradition, so when the Bolsheviks came around to help with that they initially developed Latin characters. As noted by /u/Dicranurus, this was in part due to the connotations of tsarism, as well as previous religious missionary activities that were not popular in the regions (these areas primarily being Siberia and Central Asia). There were even discussions on Latinizing Russian, but nothing ended up with that.

However by the late 1930s this program was abandoned, and nearly all languages adopted a Cyrillic-based alphabet. This would last until the collapse of the Soviet Union in 1991 (when some, like Azerbaijan, Turkmenistan, Uzbekistan, and to some extent Kazakhstan, have abandoned), but these people would have been familiar with Latin characters.

Of course it is difficult to say how many soldiers entered Poland who were from regions that had Latinization campaigns, and even if they did the letters would not correspond to similar sounds, even if they look the same (much like an English speaker cannot read Polish now). But there would be some familiarity to the script, that much is certain.