Maybe you can use the same page (login.tpl) and just remove the button from the template. Make it as a comment {*....*} if you want to re-use it easilly later.
The function will still be available, yes. In other words: people could still reach it by doing a "/user/register" in the URL. This is because policy checking is omitted for the register function within the user module (.../user/register). However, policy checking can be turned on again by commenting out the following line in "site.ini":
PolicyOmitList[]=user/register
Regarding the error message: seems weird. I just tested this with a fresh 3.3-1 installation and it works here.
I should have thought of that Balazs, silly me. Thanks for pointing that out. One question though, will it be available for a user that is logged in? (I'm not at my desk so I can't check it myself..)
Shurbann, if you comment out as Balazs said, you will not be able to open that page when you are not logged in. The rule said that all access to /user/register shouldn't be checked against the rules, so it's a kind of "allow everybody" setting..