Answer :
This is a very difficult question to answer. Being "Suicidal" does not mean that you are depressed. (I know it's weird). However, being depressed can make you "Suicidal".
Knowing from experience, having these thoughts constantly can make you believe them. Believing them can definitely depress you. So it really depends on the person. Everyone brain is different and every person is different.
Suicidal thoughts can overwhelm your brain, being the strongest thoughts someone could have. Just because someone may experience these thoughts does not mean they are depressed. Everyone goes through these thoughts, and not everyone has depression.