Between old age and childhood trauma (she's a Holocaust survivor), my grandma's memory of her childhood and family is pretty spotty. It occurred to me that this detail seemed particularly suspect, because 1) Many of the major battles in WWI took place in Poland, so he would have been fleeing into a war zone, and 2) The part of Poland that he probably fled to (Warsaw) was part of Russia at the time, so he would have been fleeing from one part of Russia to another.
It seems likely to me that my grandmother is misremembering this particular detail, but I'm curious if there's something I'm overlooking.
Edit: Just to be clear, I'm more interested in the general trend of fleeing from Russia to Poland (and to a lesser degree other parts of the world) as a means of draft avoidance (i.e., was it a thing?), rather than the individual logistics of my great-grandfather, although obviously the one might provide insights on the other.
One of the problems with tracing genealogy for Eastern Europeans in this period is that categories like Polish, Russian, or Ukrainian were quite plastic and in a state of flux. Not only were such identities flexible, but so too were the geographic boundaries of these entities. Where "Poland" started was a major issue in the nineteenth century as all the three Partition powers (Prussia, Austria, and Russia- see this fuzzy map(and why are there no good maps of the post-1815 Polish divisions!) of the Partitions) had a pronounced antipathy towards Polish nationalism and culture. In tsarist Russia in particular, there was a noted tendency of the state to minimize official Polish territory after the 1863 revolt and the state enshrined a very harsh form of anti-Polish discrimination. Educated Poles, for example, could not serve in the Russian bureaucracy inside Poland, lest they foment revolt and there were limits on Polish officers in the imperial army. In this particular case there is also the added problem of your grandmother's Jewish background. Most Jews in imperial Russia were legally required to reside in the Pale of Settlement, an area that not only included Russian Poland, but also modern day Ukraine, Belarus, and Lithuania as well as edges of Russia and Estonia. Jews after Nicholas I's reforms of the early nineteenth century were subject to conscription (YIVO has a decent overview of military service under the tsars), but draft evasion by moving within the Pale was a common way to evade the draft. Poland was technically not part of the Pale, but it was one of the few areas of the Empire Jews from the Pale could move with a minimum of restrictions. The tsarist state was quite leery to draft Poles en masse into the ranks of the Army, but what defined "Polish" could also be quite variable (language, religion, Latin alphabet, etc.) and the state set the terms.
The advent of the war in 1914 further complicates things. All three sides sought to mobilize Polish nationalism for their own ends, including setting up all-Polish units. But such paeans to a rekindled Polish nationalism also went along with a skepticism about Poles' patriotism and motives. In Russian Poland, the waves of strikes in Poland that followed in the wake of Russia's defeat of 1905 cast a long shadow over the tsarist authorities' faith in Poles' loyalty. This skepticism morphed into open hostility as the tide of the war turned against the Russians in 1914/15. The retreating Russian armies in Poland tried to grab everything of value to deny the Central Powers from reaching them, and that included whole populations of people the state and army thought would help the Germans. In this context, antisemitism merged with military priorities and served to rationalize all sorts of violent behavior. This meant a renewed wave of pogroms for Jews in the Pale and Poland as well as the prospect of a forced march into the Russian interior.
So, it is entirely plausible that your great-grandfather would have fled into Central Powers-occupied Poland over the course of 1915-17. While the German requisitions did lead to chronic hunger within the region, this prospect was for many Jews among the least worst alternatives. Staying in the frontlines risked increasingly arbitrary violence from both sides. By contrast, life in wartime Warsaw was far more stable than Zhitomir or some other Pale city near or behind the lines. Being pressed into service, whether as a soldier or laborer, was just one of the risks for being near the frontlines for civilians.
Do you know when in WWI this was supposed to have happened. Russian Poland, including Warsaw, was occupied by the Central powers in 1915. The Central Powers certainly weren't going to allow the Russians to conscript anyone in the occupied areas. If he didn't flee to Warsaw, he could have fled to the German or Austrian partitions.