Root doesn't normally effect factory OTA updates. The OTA updates will install just fine. Most of the time, you'll lose root when you apply the update. But long as you saved copy of superuser with Voodoo OTA RootKeeper app, you can gain the root back in like 2 seconds with one click. I probably received like 3 or 4 OTA updates on my Galaxy Nexus while rooted and all installed perfectly. I have not touched custom rom at all with Galaxy Nexus. I see no point when stock Google Android rom is so good.
Not on my gf's Incredible 2. It failed to install factory OTA updates. If I remember there was an error, and she also got some recovery-like error. I taught her to just clear cache every time this would happen (about once a month).
She's a saavy user but definitely not a tweaker. I walked her through doing a Nandroid once but we never really moved onto ROMs.
In the end she's not really happy about rooting her phone.
I'm guessing it varies phone to phone as you have a GNex so its pure AOSP. Furthermore maybe ICS OTA updates work differently. My gf was getting the minor GB updates like 2.3.3 to 2.3.5, etc.
Not to threadjack but I hate dealing with root in general. Rooting isn't always an easy process and once you figure it out, you could lose it with an OTA update and then have to dig for new ways. That's why for me once I root I'm on another ROM. It's easy to stick to a stable platform (i.e. AOKP, CM) and use CWM to keep updated, but dealing with stock crap? Messy.
I guess it's ok for Samsung phones because Odin makes life easier, but working with my old Motorola, and my gf's HTC? Ugh.