Bear in mind that a 'rooted phone' usually means one of two things. Simply being rooted means you have root access to your firmware (much like having adminstrator access on windows). But most rooted users are actually using entirely different firmware (known as custom firmware/ROMs), that is provided by other people not HTC.

1: If you just root your official firmware, it may work, but it's not advisable to try. And if you rooted and then installed a custom ROM, it would definitely not work. However, you always have the option of un-rooting and of removing the custom firmware and going back to official firmware. At that point you can recieve OTA updates again just fine.

2: When HTC release ice cream sandwhich it will be uploaded and available as a pre-rooted custom ROM within the day. You can count on that That said however, many of us here are already running ICS on our phones.

As you probably realise, all HTC phones have 'HTC Sense' on them, which is basically a custom UI and some extra apps that are added on top of stock android. However, many custom ROMs do not have HTC sense, for those who prefer stock android.

So, at the moment, there are stock ICS custom ROMs that are extremely good and ready for day to day use. There are HTC Sense ICS custom ROMs, but they are currently quite buggy, because they are actually based on the firmware for the HTC One X (which has ICS) that have been ported to our phone. If you want the best ICS + HTC sense experience, I'd wait for the official firmware to be released and made available as a custom ROM.

I guess I'd sum that all up by saying there is never a reason to wait before rooting. Any OTA update is available in custom rom form within a day or two.