[ale] will a Bluetooth adapter work with a Linksys Wireless B router ?

[courtneycthomas at bellsouth.net (Courtney Thomas)]

I want to connect another computer to a wireless lan the least expensive way
possible and see Bluetooth USB adapters for $1.

Can I just plug a USB Bluetooth adapter into a Bluetooth compatible windows
machine though no Bluetooth hardware devices have been installed into said
machine, and have it served by a Linksys Wireless B router ?

And can I also similarly install an identical Bluetooth adapter into a Linux
machine as well though no drivers come with the said adapter ?

As always, thanks,

Courtney