A word joiner (U+2060) added directly before or after a regular space (U+0020) should cancel the line break opportunity normally offered by the space. This seems to be the case if a word joiner is positioned directly before a space. However, if the word joiner is positioned directly after the space, LO allows a line break (unless the previous word is the first word in the paragraph and not hyphenated). In addition, if a word joiner is added both before and after the space, the first word joiner seems to have no effect at all.

After a thin space (U+2009), a word joiner properly prevents a line break from happening.

The correct non-breaking behaviour of WJ × SP or SP × WJ can be verified in the Line Break Chart of the Unicode standard (version 6.3.0):

http://www.unicode.org/Public/UNIDATA/auxiliary/LineBreakTest.html

Reproducible: always
Found in LO 3.5.4.2 (on Debian stable), 4.2.4.2 (on Windows), and 4.3.0.0.beta2 (on both Debian and Windows)

See bug 57652 for further discussion about word joiner. The issue described there looks a little more complicated, but these issues may be related.

(Bug 80000 may also be related as regards the different line-breaking behaviour of the first word in the paragraph.)