I have the most recent stable version installed (version 3.5.5375) but every time I try to apt-get install the codlite plugins it advises it will remove the codelite install.
The codelite-plugins available in the Ubuntu repositories is older than the codelite version that you downloaded from their page. So you can't have both installed at the same time using the package manager.
The good news is that (in a superficial check) all the plugins available in the Ubuntu codelite-plugins deb, seems to be included in the codelite deb available from the official codelite page.
Note that using the version from the repos has some advantages, like automated updates.
The short answer: No, you can't mix the Ubuntu codelite packages with the official packages.