With a little work you could replace Windows in that enviorment.
Linux will route all the pc's over one 56k connection. (You need a modem supported in nix) It might not be pretty if they are all doing things on the net at the same time though.
With regard to mail you have several options. You can setup linux to check all of the users mail and download it and then just have the users get the mail from the nix server. As well as que the mail that the people send out and batch send it once an hour or when ever you want it to go out.
Mail can be really tough to get working in nix if you have never worked with it before though. Especially sendmail!
You can have a look at this link for some group calendaring software
or you can roll your own application with LDAP and PHP.
It really comes down to how comfortable you are with nix as to weather it would be worth replacing Windows in a buisness enviorment. Are you responsible for it?