The only trouble with doing it that way is that your PC needs to be turned on in order to use your Wii online, and if you want to use the Nintendo Connect24 service, that means 24 hours a day
Personally, I would buy a Wireless modem router and let your Wii connect to that wirelessly. The router stays out of sight and permanently connected to the net. I use a Netgear DG834Gv3 which also gives you a built-in 4 port ethernet switch. This is, in my opinion, the best way of sharing your internet connection between Wii, PC (or PC's), Laptop, DS's, PSP's, etc..
Bear in mind though, that the DG834Gv3 has a built-in ADSL modem and won't work with cable broadband, only ADSL. However, you will haev no problems with ports, firewalls, configurations or anything else if you take this path. If you eventually decide to "hard wire" your Wii via the ethernet adaptor when it comes out, the DG834Gv3 is ready for that too.