Yes, it'll work. Your new MacBook will do wifi, specifically 802.11 a/b/g, in addition to 802.11n (assuming it was new, not for example a used first-gen new to you).
I'll add my 2 cents about Linksys. They have really gone downhill since Cisco bought them some years ago. Cisco changed out the OS and RAM on many of the Linksys products. Some Linksys models now have problems with too many connections -- e.g., if you use BitTorrent application (like Azureus) and have it set to more than 120 or so connections, then it'll bog down and crap out the Linksys router. I've also seen issues with them trying to switch between subnet mask settings, which of course makes your computers lose their LAN IP address while the router settles on a subnet mask and decides to assign new IPs.
I would recommend you look elsewhere for a router, maybe DLINK if the Apple options are too expense. I have an Airport Extreme and am very happy with it (apart from having to reboot the device after any setting change and the finicky Airport Utility).