Does morphine mean close to death for a hospice patient?

It doesn't in principle, there are, however, certain situations in which it may do so. Morphine causes respiratory depression, meaning that it suppresses the bodies drive to breathe. The body adapts quickly to this, and in most cases, in waking patients, this is not much of a problem.
In very weak patients, such as end-stage cancer patients, that are unconscious either due to disease processes or due to sedation, the respiratory depression that morphine causes may speed up dying, however.