I only tested this with Calc and xls files.
1. Open a file in read-write mode (the default).
2. Next, choose File > Open from menu.
3. Check the "read-only" box in the open file dialog.
4. Select the same file that is already open read-write.
5. Click "Open."
Result: Nothing. In particular, there is no indication that the file has changed state to read-only. I say this based on no such indicator in the window title, and no graying-out of editing buttons. (I have not checked the actual status of the file handle.)
Expected result: Mode of that file should toggle from read-write to read-only, probably with a warning that changes might be lost. That is what the very old version of Excel that I use does.
Operating System: Windows 7
Version: 184.108.40.206 release
Confirmed with LO 220.127.116.11, 18.104.22.168, 22.214.171.124 - Ubuntu 12.04 x86
Rare case, we can close the file first before reopening same file in read-only mode, but it's a misfunction
I tested writer and calc. In both cases, if the file was already open, then trying to open it again in read-only mode did nothing - the file remained in read-write mode.