Isn't there $\mathsf{CO_2}$ and $\mathsf{H_2O}$ in the oxygen-rich preburner discharge? Why aren't the Russians worried that these two would freeze when the discharge is re-condensed into the LOX inlet stream and create an ice-dryice slurry? If the RD-180 was to be done by Americans, the tapoff to drive the LOX boost pump would be from the HP discharge aft of the HP LOX pump and the $\mathsf{He}$ heat exchanger would be inside the preburner.
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Let's apply some basic logic to this.
Why aren't the Russians worried
When you design an engine there are lots of choices to be made. You also have to do lots of testing. This design survived all those engineering tradeoffs and tests, and made it into production. In production, again, this didn't turn out to be a problem.
So the Russians aren't worried because they don't need to be, because they checked and found this design did not create a problem.
My guess: the small amount of combustion products injected into the LOX may create some ices, but the particles are small enough to not be a threat to the turbopump downstream. And there aren't enough particles (compared to the amount of LOX surrounding them) to characterize the result as a slurry. Instead it's a liquid with a few particles suspended in it.
