Local subnet traffic doesn't need to go through the router, in a simple network where the entire local subnet is on the same later 2 link; broadcast ARP will resolve MACs and from there you just send your packet to its destination. Obviously no routing is needed.
However, there are two complications I can see if you are using a home router+WAP in this case.
First, if you assign a static IP that is within the DHCP pool and do not create a DHCP reservation (your router+stuff may or may not support this), the thing may assign that address via DHCP to some other host. This would create an IP conflict, causing connectivity issues pretty much at random.
Second, if you have a mixed later 2 (eg. wired 802.3 and wireless 802.11), it is possible that your router+WAP's WAP functions are filtering MAC/IP pairs that it did not assign via DHCP (instead of bridging them across the layer 2 gap). In this case, you will have to create a DHCP reservation and probably not assign the address as static on the host (instead allowing DHCP to just give the same address each time).
If your firmware doesn't support this, consider flashing with openwrt, tomato, or dd-wrt.
It is worth noting that the router on a network doesn't control what addresses a host uses. DHCP is a mechanism for doing so in a way, but it isn't mandatory and won't override static configuration.