As versões recentes, de fato, suportam, mas versões antigas podem não suportar. Para a versão 802.11n de março de 2008, Macworld escreve (grifo meu):
The Express is also the first AirPort Base Station to provide a new feature called ProxySTA. In this mode, the Express acts as a wireless-to-Ethernet bridge, extending your wireless network to wired clients.
[..]
Unfortunately, this feature isn’t documented and doesn’t appear by name anywhere in AirPort Utility. To activate ProxySTA, you must set up the Express to join a wireless network and then enable the Allow Ethernet Clients setting; both settings are located in the Wireless tab of AirPort Utility. The feature should work with any wireless network: a, b, g, or n; and 5GHz or 2.4GHz. (Note that the Express, which ships with firmware 7.3, must also be updated to firmware 7.3.1 for this feature to appear.)
As versões anteriores também oferecem suporte a esse tipo de ponte, mas sua milhagem pode variar quando não estiver usando uma estação base da Apple (por isso, não espero problemas para sua situação). De acordo com as Perguntas frequentes da AirPort Express da Apple :
Question: Can AirPort Express wirelessly extend ("repeat" or "rebroadcast") the network of a third-party access point?
Answer: No. But it can wirelessly extend the range of a WDS network that is being hosted by an AirPort Extreme Base Station or another AirPort Express.
Question: Can AirPort Express act as a bridge?
Answer: AirPort Express can act as a bridge in three different ways [..] If it is set up as a WDS remote or relay station, it can bridge the wireless network to wired clients.
Considerando meus problemas com uma estação base moderna, mas não da Apple e uma AirPort Express mais antiga, presumo que uma ponte sem fio precisa de recursos WDS da Apple (e, ao ler a pergunta 2, assumo que a pergunta 1 deveria conta também).
(Consulte também o manual da Apple no início de 2009 Apple AirPort Networks para obter mais informações.)