Yes it should work like that. I assume that you have a DHCP on your router, you should try to run a cmd on your computer and run ipconfig to know how your network is ( should be something like 192.168.X.Y / 255.255.255.0 ) then set your ps2 network to 192.168.X.(Y+1) with the right netmask and gateway. After that you should be able to "ping" your PS2 using your computer.
I never use public share for everyone, I use password + username it is better ( the "everyone" is not working nice since vista )