It will depend on how the router is setup.
For example, if the router uses a different private IP address range (http://en.wikipedia.org/wiki/Private_network#Private_IPv4_address_spaces
) than what you picked the static IP address from, then it will not connect until you switch back to DHCP. So for example, let's say that you want to connect to a router that is set to use the 10.xxx.xxx.xxx range with its DHCP but your have your computer set to some IP address in the 192.168.xxx.xxx range. In that case, it will not connect until you change something. This is actually quite possible as some routers use the 10.xxx.xxx.xxx range by default (for example, unless they have changed things, Apple routers are set to this range by default…but can be changed) while most typically are set to the 192.168.xxx.xxx range.
If the router you want to connect to uses the same private IP address range from which you selected the static IP address, then unless some other device has been given that IP address by the router's DHCP (i.e. an IP address conflict), your computer might connect…but their might be other settings that get in the way (I only really have experience with "consumer" level routers where such a thing should work…more sophisticated enterprise systems might have other features that prevent it).
Overall, I would say that you should level it as a dynamic IP address.
The exception is if you have a way to switch network settings by location. I know the Mac OS had this functionality built-in. I don't recall it being available in older Windows version, but I have not looked at Windows 7 or 8 to see if Microsoft added in such a function. I do know there were utilities that you could use with like XP to achieve this function. I can say on a Mac, I could have a "home" location that uses a static IP address and an "away" location that use a dynamic IP address…and then just select which location I want to use from the Apple menu.