Nothing like that would stop a timer. They are free running, and driven from the clock chain. The UART doesn't have a hardware buffer, but it can use DMA with serial to accomplish the same thing by DMA access to main memory. The bus arbitration for the DMA is complicated, so do you have some links to information about how the STM core uses it? In other words, where did you learn about this?
It might be simpler to just test it, than to dig through all the documentation for that. I think there is a good chance that it might work. Are you already using NeoPixels successfully with this processor? Which library do you use?