If legacy clients associate with 802.11n AP, will they get better range?
An AP-client association is half duplex, which means gains in both directions (client to AP and AP to client) are needed to sustain a connection over a longer distance. The asymmetry in transmission power common in wireless LANs (clients usually transmit at lower power than AP) can actually allow legacy clients to achieve higher data rates over a longer range when associated with an 802.11n AP the receive spatial diversity will improve the signal-to-noise ratio (SNR) from the client to the 802.11n AP, and higher transmission power of the AP will allow it to reach the client. In absence of this asymmetry, an 802.11n AP will need to additionally implement transmit beamforming to reach legacy clients over a longer distance.
