Whether Elinor finds relief in finally being able to mourn out loud (even if Marianne does not realize the two-fold nature of her sorrow) or not, I truly think that Elinor's emotion is inspired by a beloved younger sister going through wretchedness and despair.

On the other hand, I find that having gone through something myself makes my sympathy more heartfelt when I see a friend go through it after. So, if Elinor had not been disappointed in love, she might have cared for, and sorrowed with a beloved sister, but her depth of emotion might not have caused her initial burst of tears to be 'scarcely less violent than Marianne's'.