You are right that there are some ways that data can be dropped on the floor, however I stand by assessment that it is very unlikely here, assuming the computer in question is halfway recent.

Sure, in theory IRQs from the serial port can be ignored in critical sections long enough for it to matter, but asynchronous serial ports are so slow compared to modern CPUs and UARTs without buffers are so rare nowadays (even in embedded equipment (except for TTL serial ports)) that it hardly ever matters. At 115200 bps, it takes more than a millisecond to completely fill up a 16550 buffer, and that's a long time.

My empirical basis for this is that we could run upwards of 32 dumb serial ports on commodity PC hardware all transferring at 14400 bps (or more, thanks to modem compression), in or around 1993. And we know how much faster PCs are now than they were then...