If you connect to a router (wireless using encryption -- probably WPA2 in this case), but decided to set your IP yourself not using DHCP, will is still be able to access the network?
EDIT : Does the same idea apply if I manually configure the ip with ifconfig (linux or osx).
Does is recognize you as a connected user by your MAC address, or by some other authentication mechanism?
Yes, you will still be able to access the network, but if you want to access the internet through the router you will need to also set up the "gateway" and "dns" addresses in your manual configuration. You would point these at your router and it would work as if you had gotten an IP address via dhcp. This is irrespective of operating system or tool used to configure the manual setup.
Your computer will probably no longer show up in the 'connected devices' section of your router configuration as this section typically is populated by the devices that have requested an address via dhcp.
While you can restrict access to devices by MAC address, if you have not set this up then you should not have a problem. If you have set up MAC address filtering then as long as your computer is in the list then I would not expect to see a problem even if not using dhcp.
The problem would come if you are using MAC address filtering and your machine is not in the list. Depending on how well the router is configured you may or may not be able to connect to the internet.
If the filtering is done by preventing certain MAC addresses from obtaining an IP address then by going to manually configured you will be able to bypass this protection and potentially still connect to the internet. If the router is set up properly then the filtering will be on the firewall and changing to manual configuration will not allow you access to the internet.