Matthew, that doesn't sound normal. Yes, using 'nice zip' may help
(and you can certainly try it), but whether it helps or not probably
depends on
why the zip processes is slowing everything down.
What resource is the zip command using up? CPU, disk, memory? Does
running a zip command manually at the command line have the same
effect? Some tools to help you figure that out: dstat, iostat (part
of the sysstat package in Debian/Ubuntu), top, vmstat, mpstat.
My wild guess is that your zip command is tying up your disk I/O
rather than your cpu, as in my experience, that is more likely to
cause obvious system-wide lag.