AVI: Index is at the end, so it might play fine in a tolerant enough player.
MPEG-TS: Headerless. Will play fine in any player.
MP4/MOV: Index is sometimes at the end; if so, it might play fine in a tolerant enough player.
MKV: Has a header and index, usually at the start. Probably won't play.
Ogg: Has a header, but is indexless; might play fine in a tolerant enough player. Probably not though, as both Vorbis and Theora (the only things Ogg supports that are ever used) both rely on custom Huffman tables in the headers.
Try it with some broken files sometime. It really is amazing. It may not be capable of seeking properly, but it will have a damn good go at playing the file.
Also - the frame index of an AVI file is at the end. It is only the headers which are at the start, and these are less important.