Will all of the gas in the universe be converted into red dwarf stars?
No. The reason is that gas recycling only recycles only about 40-50% of the gas in a sun-like star, leaving the rest as a white dwarf that slowly cools off. Heavier stars are even less effective in converting their gas into a condensed core. So the process will tend to produce a fair fraction of heavier white dwarfs now in the early stages of the stelliferous era, followed by a slow emergence of lighter white dwarfs from red dwarfs in the rest of the era.

Adams and Laughlin estimate that the final mass fractions will be brown dwarfs (never fused) 9.7%, white dwarfs 88%, and 2.4% neutron stars and black holes. In the post-stelliferous era some of the brown dwarfs will merge and make a few extra red dwarfs .