Yeap, adding the noindex tag will remove that page from google results.
And no, there is no guarantee that rankings will improve nor go down by adding the noindex. It is just the patch in order to do not appear in search with a page you dont want to show.
You should anlayze those incoming visitors to the log-in page and try to figure out wherer they were looking to log in into the web or anything else.
Also, consider the idea that removing from index that log in page, will make those visitor to do extra interactions with your website in order to log in. Is your UX prepared to that? Have you analyzed your audience for that?
As you can see, there no simple answer, because you must take into consideration the intent and usability for those visitors.
Hope it helps.
Best luck.
GR.