This question has been discussed a couple of times on the AOPA forums (members only) and the conclusion there was that it's completely fine to trust the automated identification. If the system is fully certified for IFR then why wouldn't you trust it? And if you don't trust one specific feature then why should you trust any of them?
Identifying NAVAIDs correctly is in the instrument PTS but the FAA doesn't require any specific method of checking. In my last instrument checkride I used a G1000 and the DPE had no problem with me using the automatic identification; that's what it's there for.
Having said all that, things can and do go wrong, so cross-checking against other sources is still a good idea. For example, when you load a VOR approach from the database, the G1000 will automatically tune NAV1 to the NAVAID frequency and identify it. If either the frequency or the name doesn't match what's on the approach plate - or if the name is missing because it couldn't be identified - then something is wrong and you need to investigate.
Ultimately I think this is a question of comfort level, both personally and with the equipment. Some people will check the morse ID directly every time, out of habit or preference. Others won't, because they're confident that they know the equipment well enough not only to trust it, but also to identify and handle any problems.