No you won't because a G wireless is up to 54 Mbps (Megabits per second) or 6,912 KBps (Kilobytes per second) or 55,296 Kbps (Kilobits per second)
The nice thing about wireless N is that it uses MIMO technology and up to 3 antennas on the PCI adapter card and on the router.
N routers are great for home networking the computers together but at your speeds I don't believe it would be an advantage.
Your price is high for RoadRunner, here in Austin, TX you can get 17 Mbps @ $35.00 per month plus 54 different taxes, user fees, gov't fees, subsidies, etc. fee this, fee that, here a fee, there a fee, everywhere a fee fee!
TrainableMan is correct, the only true way to test your RR connection is through the LAN port via ethernet cable to the modem or router. That will give you your truest test speeds.
IF RR is supplying your wireless router/modem setup I would just have them change it out and have a modem only, then purchase your own wireless router. You'll probably get a little better pricing on you service too.
Plus then you can get a damn good router instead, plus you're probably paying rental fee on the RR router anyway. I recommend either D-Link or Belkin routers, they usually get top reviews. But as with AV software there are a plethora of opinions out there about wireless routers.
Actually, the pricing is different in each market. I'm getting 7mbps for what I was paying for 1.5mbps. I had put in an order for all services to be stopped, then the request landed on the regional manager's desk, because I had been rightfully complaining about my service. That's why three hours later, I got an unexpected call from them. See, I was fed up with them to the point that I called to disconnect, without even having another ISP lined up. My landlord told me that I could use theirs anytime that I wanted.
So the regional manager asked me what I wanted to keep me as a customer. No one had ever done that before. I told him all that I wanted was what I was paying for, no more, no less. I also told him that I no longer wanted the phone and TV, the internet only. Then he said the price, $44.90 for 1.5mbps. I said no, I was paying for 7mbps, and if I couldn't have that, to cut all services off. He agreed with me, giving me what I wanted. And technicians came by and checked everything out, getting rid of those "rat nests" of wires where former tenants tapped into the landlord's connection while they were at work, and even rode the neighborhood, finding at least a couple of sloppy pirated connections that caused leakage for everyone.
While $44.90 sounds high for your area, it's the standard price for Road Runner Lite in this one. And I called AT&T to see if they could match the price, as soon as I did, there they were, trying to shove a phone line down my throat, at a cost of $29 monthly, not counting taxes or internet service. I told them that Time Warner didn't force TV service on me to have internet, why were they trying to force a phone line that I didn't need on me. I was told that to have internet, you have to have a phone line. I told the rep that they were trying to return to their former days, but now there's competition in town now. He politely suggested that our conversation was headed nowhere, and there was no need for further discussion. I agreed, and hung up. BTW, AT&T's offered speed was only 3mbps at a total cost of $79.99, plus those 12 pages of taxes & fees. Plus, AT&T has a clear "abuse clause" in their deal, if you go over a certain amount (I don't know how to calculate this), you're moved up to the next price. I don't have that, unlimited is unlimited for me, although if you use a lot, they will "throttle" you during peak usage times. I get around that by using my landlord's connection.
But $44.90 for 7mbps (including taxes & wireless router) is cheap for this area, I've looked and looked, and no one beats it. No one even comes close.
