You won't see much wildlife on that trail for how short it is and for how loud your group will be from talking and walking. If you want to carry spray for peace of mind go for it, but I've never been worried about running into bears there.
I haven't been there in November, but the people I've talked to when I've been there have said that the only wildlife they've ever come into contact with were mice. Some of them have been going up there on a regular basis for years. I would still recommend being prepared, both for wildlife and weather.
There is always a possibility. Bear spray is a good idea. I've been there 4 times and haven't seen one yet though. Be careful.
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