Yes, it will work. However, the logging function won't save data to the correct page. Right now, each user that clicks the log button will store their own separate copy. So if 5 different users do it, 5 different copies will be created. What the part in Common.js does it specify a common page such that there is only one copy for the entire wiki. Also, you can set it to autolog the data for you so you don't even have to press the button.
I am not sure what you mean by "removal". Staff look at the JS and if they determine it is not suitable, they can do one of two things.
If they see a quick fix, they may do that for you and then immediately approve their modified version. On a few occasions, I have seen them do this for simple syntactical errors as well. However, this is not a service they have promised to provide. There have been a few times that I have made a mistake and it got approved.
Otherwise, they will simply mark it as rejected and the most recent approved revision will be used instead. Typically they will provide a reason for the rejection so you can try to correct it and resubmit for approval.
FYI, I went ahead and copied the previous day's data from your personal log to the wiki's log. If you don't want extra pages laying around, you can go ahead and delete your log and Monstermon's log. Neither will be used now that the wiki's log is the target. Also, there are additional settings you can set so that it automatically logs the data when either of you access the wiki. That way, you don't need to remember to click the button each time. You do need to visit the wiki though. If you are interested, you can enable it by editing your site's JS to be like this: