Uhhh ... orthogonal ... right (computer folks :turned:)
The thread I linked called Compatibility and You explains mod conflicts better than most sources (which is why it is a pinned thread). As bgs408 explains each entry in a mod is a record only one mod at a time can effect any one record. Hence you may have several mods that affect face data, but that might be OK and often is because faces can have several records about them. So I can use TNR, eyelash mod, various hairstyles, facial features, texture replacers - but still each record is only going to be affected by one mod at a time.
The way I like to look at it is the Oblivion.esm is the base game - called vanilla. Each mod after that (even DLC) are conflicts with the base game that are designed to win (the conflict that is over records). All mods are conflicts with the base game. Mods that load later (and therefore win) are conflicts with the mods that load earlier (and lose) provided they both ouch the same records. Conflict does not technically mean game breaking but some modders so hate anything in their mods being altered further that they will call anything that changes them conflcits and imply breakage. On the other hand - yes some mods can and do break each other.
FCOM is a series of patches that make overhauls work together - Wrye Bash is a tool that helps facilitate that and has since grown into helping with all sorts of conflicts and allowing for very complex combining of mods.
Or more simply: yes, of course, and no not in a game breaking way. That is unless your going to call up the straw man of game balance.
I'm of the sort that think that most overhauls (not that there are a lot really only a handful) touch too much. My wish is for overhauls to mainly address scaling and leave combat, stealth, magic, leveling, and quests alone. But it is just that way when trying to rebalance a game - the desire to keep going. But the problem is parts can become outdated or encumbering to keep patching - causing updates and extensions to take years to complete. Such is the state of most of them. Like the option to use living economy in FRANS ... the better option today is Enhanced Economy. But since people flock to overhauls (wanting more and more) they miss that or then experience a learning curve in finding out about it. Lyrondor is not bad (better than vanilla) but not as good as other things to come along.
Most load orders I see rarely have just FCOM - they also include many other mods. As bg wrote at the end of the first post in scaling overhaul comparison:
This is one thing to keep in mind: Overhauls do much, they're keeping the game alive and playable for many of us, but none of them is a "full happyness package". Whatever mod you choose, you'll be able to enrich your Oblivion experience with even more mods
The tool that will help the most is called BOSS: Better Oblivion Sorting Software - it will help place things in the right order and of course it handles FCOM and every combat mod out there.
[edit] fixed my link above