That is exactly what it means. The Father can neither dwell within us, nor lay down His own life, because He is already a perfected, immortal being. The Son offered Himself to fulfill the Father's plan, and the Holy Spirit did the same relevant to His role.
The Godhead exists out of necessity. The Father, being perfect in every way, would not have introduced roles and members of the Godhead that He was capable of filling on His own. This is also another reason that it can be rightly said that the Father, Son, and Holy Ghost are one God. None of them possess the capacity to bring about the salvation and exhalation of man alone. Hence, united, they operate as one God.