My recollection of the performance of communications at the time is a bit different.
In the late 1980s the 16550 was pretty common and a welcome upgrade from the 8250. However most machines still topped out at 115,200 bits per second which was limited by the UART. If you assume no protocol overhead or errors that is 14 kilobytes per second. For comparison a 360KB double density diskette drive can do around 11KB/sec. And the machine would be close to useless while you did anything because you'd be furiously polling the UART.
Ethernet, via the inexpensive NE1000 card could do around 60KB/sec, which is far faster than anything using the serial port. And the effective throughput would be faster too, as you'd be re-transmiting less. Office environments were definitely using Ethernet or other packet based network cards, not cobbling together parallel port and serial port networks.
Those cards did not have deep FIFOs, TCP/IP offload, or anything. We're still using those same exact cards on retro machines today, and they performed the same way back then. Compilers were not that much different either; the mTCP numbers for when it was compiled under Turbo C++ are about the same. It's not sensitive to code generation, as most of the sensitive parts (IP checksum) have to be done in assembly anyway.
Back then they would have used something lighter weight, like IPX. TCP/IP would have been overkill so it was not commonly used unless your office was connected to bigger things.
As for the 286 ... even an 8086 with a good Ethernet card can hit 150KB/sec using Ethernet. With the standard card of the day, a 3Com 3C503. The 8086 has a 16 bit bus comparable to an 80286 but a less efficient CPU implementation. An 8Mhz 80286 should be even faster.