Not necessarily.
Depending on your internet connection (mine is dialup),
surfing using the parallel port is plenty fast enough.
Considering even on a fast dialup connection (50K a
second), the parallel port easily has that much bandwidth.
Before I had a router, I used my A4000 connected directly
to the MODEM through a GVP IO serial port. Then used
PARNET (running SOCKS5) to connect my A3000 to the
internet.
Lamar