Yes of course if you desire that capability. A wireless router will still have some wired/ethernet ports available (typically 3-4) if you desire some wired connections as well.
You mentioned a Linksys WCG200. First, my advice is to avoid those all in one gateway devices and always go with a stand alone router and separate a modem. Second, that device is an older model and it has been classified as being "end of life" as of 3/09 on their Approved Modems List.
The router is basic, but would work. Keep in mind that it is a "G" router. If you have any newer PC or laptop that is "N" capable, it will bump down to use "G" and will not get its full potential transfer rate.
So, the best you can do is Wireless G. Your Router should support that as well as Wireless N.
If you want the faster speed of the wireless N you should be able to swap out the Wireless adapter to get the wireless N speed.
The easiest way to find out if an "N" wireless adapter is available for your laptop, is to search upgrades on the manufacturer's website. Once you have identified you can replace it & you know which one you need, you can shop around on Ebay or vendor sites. Swapping it is usually simple. Access to the card is normally under the laptop behind a removable panel.
How do I swap out the Wireless adapter to get the wireless N speed ?
If you have a laptop, go into device manager and disable the Broadcom WLAN adapter.
Procure a Wireless N USB adapter that you can plug in to one of the USB Ports.
If you have a desktop with an Integrated Wireless Adapter then the process is similar to that of the Laptop with the exception that you would then have a choice of a USB adapter or a PCI plugin adapter.