This involves multiple different questions.
The first big one is whether you should trust SmartThings for this type of a life-and-death situation, and I think the answer is clearly No. In fact just about every Zwave manufacturer has a note in their user guide that the equipment should not be used for life and death situations. There are inherent issues with mesh itself, but on top of that smartthings just fails too often at the present time. The company is very aware of this and have made improving reliability their top priority, but they're just not there yet.
Just in the last two weeks there have been four major feature failures, including a change to the platform breaking the functionality of the minimote, which is the handheld button controller that is the official recommendation for using if the Internet is not available. It was down for about a day.
So, I definitely wouldn't do this with SmartThings at the present time.
Automatic Door Closers for Everyday use
There are several automatic door closers on the market, most often used by people in wheelchairs, that are quite inexpensive and very reliable. Skylink that makes a nice line.
However, all of these have built-in safety features which would probably make them unsuited to the emergency case you describe. They close very slowly, about the same speed as a garage door. So while you could have one, I'm not sure it would fit the use case you're thinking of.
Then there are panic rooms. This is what very rich people have, or people who know they are likely to be a target. You can definitely get these with doors that slam close quickly and reinforced barriers and separate cameras and all kinds of stuff. It's just that they tend to be really expensive. But you can find plans on the Internet for do it yourself versions with various feature sets.
Panic rooms definitely serve a purpose for some households, but in terms of a typical burglary, sirens and lights are probably just as effective.
If you don't have kids, one of the best things you can do is put a solid door on the bedroom with a good lock. It's amazing how many bedroom doors don't have locks or are extremely flimsy. This doesn't even have to be a smart lock. Just lock it when you go to sleep at night. That would slowdown most non-professional home invaders long enough for you to get a call out to police. Note however that this kind of door would slow down first responders responding to a medical emergency. So you have to weigh the pros and cons for your own household.