Should be, assuming your Internet connection is sufficient. I have a PS3 connected via wireless for pretty much the same basic purpose. Firmware updates, and I bought a copy of Final Fantasy 7 and 8. Don't use it for online gaming at all, and it works fine, but it's also backed by a 7Mbps DSL connection.
Any issues with this? The only internet access I'd use are mostly for the channels, maybe to purchase some stuff through the Wii's channels, but I don't really plan on playing any games online in real time. Would this be fast enough for that use?

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