Maybe. Maybe not. On two occasions I've had a major adrenalin dump (heart beat racing, blood pressure above 160, hands shaking -- the whole nine yards). People aren't always cool and calm when under extreme pressure. The mind focuses on what it believes is most imperative for surviving he situation. You don't have time to think about secondary issues.
If the house was on fire, my first priority would be to get my wife out of the house. If my wife was having a medical emergency, my first priority would be to get help on the way and then give first aid. I could easily see myself forgetting to put a gun away in either of those situations because it just would not be a high priority.
I disagree. I think the jury would be very predictable and you would be convicted. If police found an unsecured gun in your house it would be almost impossible to win the case. If your lawyer can not get the search thrown out, I think it would be plea-bargain time.
While I suspect that the judge would not apply anywhere near the maximum sentence, I suspect that the you would never get an LTC again. In fact, even if you did win the case, I would expect the chief to revoke your LTC on the basis of suitability.
Given my view of the relative risks and the ease of using a fast-access lock box, I keep my gun locked up. YMMV.