Is it possible to keep OO.o by simply omitting the line

sudo apt-get remove openoffice*.*

and, if so will they run happily alongside each other without conflicts?

No they will conflict.

I'm running LibreOffice, the release candidate, and it seems remarkably stable to me. In fact a number of bugs I'd encountered in OO.o 3.2 seem to have been resolved.

I don't know what release candidates you've tried in the past, but LibreOffice is a mature product, being, more or less OpenOffice.org with the proprietary components removed (the logos and other trademark items, not code), and the inclusion of code from several other forks of OO.o, that ca never be included in OO.o due to copyright assignment issues (Oracle, like Sun before them, require that developers assign copyright to Oracle, some independent developers and all competing corporations refuse to do this, hence the forks). The Document Foundation does not requires copyright assignment, which means more individuals and more corporations, like Red Hat, IBM, Canonical and may others, have no issue with contributing code to LibreOffice, and LibreOffice can also use code from OpenOffice.org, which means Libre Office will impriove faster, gain necessary and useful functionality faster, and to the exclusion of OpenOffice.org.

In short I think you will find LibreOffice a significant improvement on OO.o 3.2 already. This being Linux, if you do have problems, it's a simple mater to remove LibreOffice and replace it with OO.o using "sudo apt-get remove libreoffice*.*" and "sudo apt-get install openoffice"