No - absolutely not.
The address translation does not care about DHCP/Static addressing on the private side.
Just give everything a static IP address (make sure you use the right network!)
Eg. If DHCP gives you;
IP Addr 192.168.1.5
Mask 255.255.255.0
Gateway 192.168.1.1
Then use 192.168.1.[say 10 - 254] for the address and leave everything else the same.
Check with your ISP for the DNS servers and statically asign those as well. For your internal nodes just put everything in the hosts file. This should work fine.
