Yes, of course it is. What you are describing is merely a story in which nobody speaks. Since it is perfectly possible to have a story in which a character is alone the entire time, why would it be a problem that there is no dialog?
Dialog is just the recording of a particular action: speech. You might as well ask if you can write a good story in which nobody eats or sleeps or fights or makes love or falls out of a tree.
If a story has story shape and is well told on a serious theme, it will be a good story, regardless of which actions characters take in the course of it. (Serious here does not mean not funny. It means takes the depiction of the human condition seriously, which can sometimes be very funny.)