Yes, taking away someone's guns may prevent one method of suicide, but it won't prevent suicide per se. Especially now with all the publicity about Epstein, millions of people learned how to kill themselves simply and relatively painlessly with just items found in any home, a doorknob and something to put around their neck. All the reporters have been bleating exactly how to do it and how the person loses consciousness almost immediately and then dies shortly thereafter.
Substitution effect--far too many drugs, cheap alternatives such as plastic bags, razors, etc. exist. Japan makes it almost impossible for folks to have firearms but has a very high suicide rate that last time that I checked. Once again the tool is not the deed as far too many magical thinkers believe. A gun is an inanimate tool, no more no less, and the person acts on it rather than the reverse until at least Googul Nest folks start making smart internet guns.