Short answer is Yes.
In 802.11b mgmt traffic is always 1Mbps and payload, if enabled, is at the higher speed. Payload speed is determined by AP and client configuration. If AP has enabled more then one speed then client will connect at highest speed with signal/noise ratio higher then preset value. If two clients connect at different speed, then AP will work with each client at the speed client is connected. That means 1Mbps client will slow down 1-11Mbps WLAN while it has traffic exchange with AP.
