802.11n-supporting devices are supposed to be backwards-compatible with 802.11g and 802.11b, but it is possible to configure them in ways to refuse to work with older protocols. The default should be that it will support all previous protocols within the same frequency band, however.
The main thing you need to make sure of is that it's receiving/re-transmitting on 2.4 GHz band.
802.11n actually supports both 5 GHz and 2.4 GHz band. A device that fully supports the entire spectrum of 802.11n supports both frequency bands. A device that supports only 5 GHz would only be able to retransmit 5 GHz signals, which would be 802.11n or 802.11a. But if it supports 2.4 GHz then it should be able to work with 802.11g.