I am currently contracted by a bushian that provided me with my ARC. My contract at my bushiban expires end of Feb and my ARC end of March. My problem is this - I am starting at an elementary school on 14 Feb - before my contract at bushiban expires. I am going to Thailand for CNY, and would like to arrange my student visa while I am there. If my student visa (on which I will be working at the elementary school) then replaces my ARC, I will be working at my bushiban for approximately 2 weeks without an ARC, and without them knowing that I do not have an ARC.
What are the implications?
Also - what documentation do I require to get a student visa?
What do you mean here? A student visa is (usually only) issued if you are studying at university/private language school here in Taiwan AND at universities anyway, one only qualifies after 4 months of study.
Once you leave country and return, you will have a least another 30 days upon reentry to figure things out. As for your school knowing u don’t have an ARC, i’m sure they don’t care. The 4 schools i currently work at don’t anyway. 
Is there even such a thing as a student visa? Being a student is a way to get your visitor visa extended, or apply for a resident visa (which gets yo an ARC, I thought).
But if you have a visitor visa, you’re working lllegally, and I wouldn’t have thought a secondary school would let you do that?
No, there is no such thing as a student visa but the term gets used a lot anyhow. There is only a visitor visa with either “pleasure” or “study” checked as the purpose of your visit. And from what I hear, you don’t want to be checking “study” unless you have paperwork from a Chinese school showing that you are a student. Otherwise, you’re probably setting yourself up for a hassle.