802.11 wireless communication uses the lowest common denominator for negotiating speeds.
The receiver sensitivity/speed of the AP you are referring to indicate what speed the user will connect if the signal from the client (STA) is received at that level. Your wireless NIC will have similar sensitivity specifications. Therefore the reverse is also true. And therefore, the AP and client negotiate speed in their initial "conversation", along with security settings, etc.
If the AP sees client A at -90db, he will negotiate with that client to be 1Mbps, for example. Unfortunately, a single AP can only talk at one negotiated data rate for all users, therefore when client B attaches at -70db, client B's negotiated data rate will still be 1Mbps.
Nailing up the speed of the AP to 1Mbps will not increase the range, it's simply a function of the RSSI value (that db thing) with respect to both the client and AP.