Maybe. Maybe not. Is your wireless router Netgear? If so, your chances are better. Netgear publishes compatible adapters in the routers documentation. Most problems with setting up a network are ability and compatibility. And even if they are able and compatible, will you set the right switches to make it work. This is where most people fail and return their networking devices as defective. Refurbs offer great bargains.
Keep your eyes and searches open for wireless gaming adapters. They are the easiest to set up and most stable. Should be able to find one for about $30 delivered, eventually.