"..can the router work just as efficiently withut this extra expense..."No, but whether that matters to you depends on what you want to be able to do.
Pre N is backwards compatible with wireless B, and wireless G which is backwards comptible with wireless B - if you already have such an adapter you could try it and see what you think.
For internet access to work at full speed with a high speed modem, wireless B or G/B is fine - it doesn't matter which you use - the max internet speed will not be affected.
If the network adapter is USB connected, it doesn't matter if the device or the USB port are rated only 1.x - the max internet speed will not be affected.
However, when you have more than one computer on your local network, if you want to be able to transfer data at the max possible speeds bewtween computers, wireless B is much slower than wireless G; wireless G is much slower than Pre N.
Wired 100mbps is faster than wireless B, or G (54mbps).
Wired 1000mbps (Gigabit) is ten times faster than Wired 100mbps.
Only Pre N is faster than Wired 1000mbps (Gigabit).
All network related devices, and your internet connection max speed, are rated in megabits per second, not megabytes per second. Allowing for 8 bits per byte, and the equivalent of a couple more bits per byte for error correction and other network overhead, you divide the rating in mbps by 10 to get a good approximation of the max data transfer rate in megabytes per second is.
And there's the matter of reliability of the wireless connection - whether it will lose it's connection for no apparent reason.
You may have no problems with wireless B or G, or you may have a lot of problems.
Wireless B is much less reliable than wireless G; wireless G is much less reliable than Pre N. None of them are as reliable as a wired connection, but Pre N comes pretty close. It's recommended that if you have a home network connected to the internet, at least one computer should be connected via a wired connection for the greatest internet connection reliability.
Wireless B and G use 2.4ghz - so do a lot of other devices, such as wireless phones, "walkie talkies", etc. 2.4 ghz is the "carrier" frequency - each 2.4ghz device actually uses a frequency slightly offset from 2.4ghz, devices made by the same manufacturer use a different offset for each device, but depending on what else you have that uses 2.4ghz, there are only so many offsets that can be used, and you may have problems with other devices interfering with the wireless B or G if the other device(s) use the same offset frequency, or one close enough to conflict.
Pre N uses a higher Ghz a lot less likely to interfere with other devices, but it also supports 2.4ghz for backwards compatibility with wireless B and G.