Every time another OTA comes out, people who modify their phones ask the same question. I've written up a FAQ based on the past OTA's.. -> http://mark.cdmaforums.com/MotoX-OTA.html
if you want to read it to get more info.
Part of the issues you are talking about when taking an OTA is that the OTAs want to patch and replace only SOME files on your phone, so it checks to make sure the update is for your phone and its android version by evaluating certain files on the phone, that they exist and that their check sums match what the update expects.
i.e. change/modify/delete files the OTA update checks before installing, and the OTA will refuse to install.
If it didn't do this, the wrong update could possibly flash to your phone, replacing files with incompatible versions and making a big mess.
So yeah, "getting back to stock" (or as close to it as you can) is always recommended before taking an OTA so the "check" doesn't fail and prevent the OTA from applying.
In the past, freezing apps with Ti Backup was enough of a modification to cause the OTA's to fail. So often it is still suggested to un-freeze those done with TiBackup.
The OTA zip file (as downloaded) will only flash from Stock Recovery. TWRP and CWM for example don't properly process and flash them, so if you try to install when stock recovery is NOT on your phone, you get stuck in a bootloop. Using mFastboot to flash stock recovery back on is fine for those with unlocked bootloaders. Locked Bootloader users, is another matter.
There is a way "side load" the OTA, IF you have stock recovery, your phone hasn't received the push from Moto or your Carrier yet, and the OTA Zip file has leaked. But it still requires you get back to stock, etc. just as if you were getting it OTA.
My Moto X tips and info
Currently using Verizon Moto X Developer Edition
on my personal line.. But I have too many devices to choose from for work and personal... For the full list click -> HERE
Sign up for Dropbox -> HERE