Yes, if you sync both your home and work desktop the bookmarks from the home desktop will be combined with the ones from the work desktop and vice versa.

In the very early days, I got the sync relationship set wrong somehow and instead of merging it went one way the wrong way. That's probably fixed by now, but just in case, I do suggest making an extra backup of your bookmarks. This article has the steps for that: Restore bookmarks from backup or move them to another computer.

I do not use Sync with my mobile, but based on a different thread, Firefox keeps track of the sources of the bookmarks and may show them in a separate folder rather than, say, merging two folders with the same name together. That probably makes more sense because the Android version does not have the same level of sophistication of bookmark organization as the desktop version.