He does have depression as far as I know. Suicide isn't an unreasonable thing for any character, let alone Matt Murdock (you can have depression without contemplating suicide, but anyone is capable of feeling low enough to commit suicide given life events, propensity to depression, etc.) To me the key thing is the method and this is where I am going into specifics so probable triggers.

I don't see Matt as a pills or hanging guy or even the type to slash his wrists. It strikes me that if Matt were going to reach the conclusion that suicide is the answer he would do it with brutal efficiency - no second chances.

I also see Matt as being very proud and this pride could go in two directions. The first direction is that he would not want his friends to know that this is the choice he had made, he could even dress it up as protecting them/ not wanting them to blame themselves. The second way that pride could go is "Look! I can do this right!"

I mainly think though that it would not be a conscious decision with Matt. He may think that the world is better off without him in it and he may become more reckless because of this, either to prove to himself he is worth something or because he genuinely no longer cares about himself. He may even plan out different methods, but even disregarding his Catholicism, I don't think he would do it without third party involvement, be it criminals or police.

I think he would see it as being far better to go out like his Dad, one last grand sacrifice knowing it would lead to his death.