Yes, a determined suicide will usually find a way. Hanging, obviously, is both effective & the means are basically universal. Even in prison. But a number of studies have indicated that means reduction does reduce the number of completed suicides. This idea originated in Great Britain after the country switched from lethal coal gas to natural gas. Rather than seeing suicides alter their methods, the number of suicides overall decreased in subsequent years.

Here in the US sleeping meds are far less toxic now that barbiturates are no longer used. I do believe a reduction in the accessibility of firearms, esp handguns, would reduce the suicide rate overall. To what degree is anybody's guess.

https://www.hsph.harvard.edu/means-matter/means-matter/saves-lives/