There are two kind of firewalls: software and hardware.
The first type is usually integrated inside modern operating systems, either like stand-alone apps (such as in windows) or straight intro the kernel (such as Linux or Mac OS's).
Unfortunatelly, every peace of software out there is not perfect, so bugs and problems may appear out of nowhere, sometimes when you're least expecting them.
If this can be ok for the normal home user, for a firm that depends on its internal system security (and by ssytem I'm not reefring to only one computer) it's actually something that can't be accepted.
Of course, the chances for this to happen are very few, but it doesn't assure anybody that if they are going to use it they will be safe.
Hardware firewalls are devices strictly build for this, and nothing else. They usually are integrated into high-end routers, but they also come separetely.
I'm not going to talk much about them, so going straight to your question:
If you are sure that all the pc's from your local network that connect through your router are safelly protected from viruses and spyware then by all means disable all the firewalls from the clients and use the one that comes with your router (even if it's software).
In case you're not sure, it's like protecting a castle from the outside invasion when the enmy is already inside.