I don't think AA will expect your husband to wait 4 hours for the bag, so if you can see it's being tracked I'd just go home if there is no-one there and fill in the online forms. But it may give a bit of reassurance to get it reported in LHR if you know someone is coming soon.
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One of the annoyances I have in this space is when people make say 2 unspecific posts about a travel problem, get some good advice or commentary and then we never hear from them again. So I'm quite comfortable getting a perhaps more insight to the poster's thinking and reactions, perhaps in more detail than normal. I do think it's just a weather irrop which was fixed by AA a bit better than I was expecting, so that was also interesting, but ultimately falls into the "stuff happens" category rather than anything major, but obviously we can all think of previous circumstances where that didn't work out. It sounds like a fairly limited irrop, if thousands and thousands of passengers were affected then the system isn't always as customer friendly.