Anyone who has dealt with depression can tell you how this works. The suicidal urge doesn't last very long, but guns are waaaaaaay too convenient. Guns are far from the only way to kill yourself, but their widespread availability and the immediacy of the action are unique among suicide methods.
The theory sounds right, but it doesn't look like the data supports it.
We have a waiting period here in the USA when you purchase a firearm from a store. Is the waiting period not long enough in your opinion?
There had been a Federal waiting period, but it was ruled unconstitutional in 1997. Some states have waiting periods. See https://en.wikipedia.org/wiki/National_Instant_Criminal_Back...
This isn't so much about "I want to kill myself; I should go buy a gun" but rather about "I want to kill myself; my dad keeps a gun in his sock drawer". Talk about responsible gun ownership all you want; but if you own a gun for personal defense (as the majority of gun owners do), it's probably not locked up most of the time.
In addition I have this philosophy that if you want to interfere with peoples freedom you are responsible for making their life (as judged by that person) worth living - not just preventing them from killing themselves.
Regardless, it would be interesting to know if there was data on the effect on suicide when you get increased gun control. The data for suicide that I have seen seems to imply that the availability of guns would increase the suicide rate for men, which is also the biggest demographic for suicide victims.