The thing I discovered was that I caught on fairly quickly just based on all the reading I was doing in British books. I suppose it will depend on your lecturers, but we used the Harvard system of referencing and we were reminded to be careful with grammar, but as long as things made sense and weren't obviously misspelled, it had no consequences. I had one paper come back with a couple of words circled and the word 'grammar?' written in red in the margin, but my mark was good...
I also had one lecturer who reminded us that American spellings are becoming more common, aside from the fact that the sources we were expected to use could come from anywhere in the world. For instance, on the subject of 'globalisation', he reminded us to look for it with a 'z' in it because that's the more common spelling.
So, no ripping apart of papers for me...hopefully, you won't take any flak for your usage since you probably won't be the only 'foreigner' in your program, and possibly there will be other non-native-English speakers in the course as well...