No way. I get the thought process, but if it's not knives, they'll jump in front of a vehicle, tie a bag around their head, etc. If you want to kill yourself, you'll find a way. If your fear is of someone using it against you or another guest, they can just as easily bring their own or worse, a gun. Knives are relatively cheap. They could purchase them, go in the bathroom, come back out. Hell, you can use a pen as a weapon if you wanted to. Then there are things like shovels and those heavy dumbbell weights.
As far as this particular case is concerned, this would just be putting a band-aid on a gun shot wound, anyway. Fix the problem. Psychiatric support is something society looks down on, and often, people won't attempt to reach out for help because of that. Mental health in America is in a very sad state, and we need to do more to get help for anyone who feels they need it.
Also, we should have a right to die. It's a murky subject, but it's your life should you choose to take it.