You can bet whatever you want, but if you could maybe find a study on that, it would be a lot more helpful.
I won't hold my breath though, even if what you guessed were true, there is almost no funding for studying this issue so I sincerely doubt you will find such a study.
About the funding issue:
And just to respond to the response I usually get to that, back when there was some interest in the issue it was found that: "one common explanation of the sex difference in both types of suicidal behavior is that males use more lethal methods and therefore they are more successful. These differences, however, are not the complete answer since when method is held constant sex differences remain"