I looked this up in the C600 user's Manual.
No.
When a Comm Slot Modem is installed it disables the modem serial port.
I also checked whether using an ethernet card (PCI based) in the Comm Slot reduces the PCI slots available, but it did not say so, so I assume not. It appears that four PCI devices could be installed in the C600 and by extension, in the 6400.
According to Everymac.com these are Alchemy architecture. I think we've been calling them Tanzania, but unless Everymac has it wrong, they're Alchemy. The 6500/5500 is Gazelle.