Learn English – Should I use the question sign in a phrase started with “I’m wondering…”

The syntax you want to use doesn't sound natural to me (also a native speaker) for an indirect question. What you seem to be asking is a direct question: I'm wondering, "What is the time?"

This site gives instructions on how to make an indirect question. And this one an explanation of how embedded questions are formed.

Perhaps you could use ellipsis.

In reported speech, the ellipsis is sometimes used to represent an intentional silence, perhaps indicating irritation, dismay, shock or disgust. This definition is more known with younger, internet savvy generations.

or with a different use from the same Wiki page:

The ellipsis is one of the favorite constructions of Internet chat rooms, and it has evolved over the past ten years into a staple of text-messaging. Although an ellipsis is technically complete with three periods (...), its rise in popularity as a "trailing-off" or "silence" indicator, particularly in mid-20th century comic strip and comic book prose writing, has led to expanded uses online. It has been used in new ways online, sometimes at the end of a message "to signal that the rest of the message is forthcoming.

Because formally the question is not about whether he is coming, but about what you think.

Pragmatically, it usually does have the same meaning as the other examples, but with a different embedded question that may not be so:

Do you think I should go?