The implicit answer is "no." This question can be written as a statement. Alternate translation: "Hope will not go down with me ... dust." or "I will no longer hope when I go down ... dust." (See: [[rc://en/ta/man/translate/figs-rquestion]])
Sheol does not really have gates, but it is a metaphor for Job entering Sheol. Alternate translation: "when I go into Sheol" (See: [[rc://en/ta/man/translate/figs-metaphor]])