I would say yes. Some of the things said by the Angel of the Lord could not be said by an "ordinary" angel. For example:
NKJV Gen 16:10 Then the Angel of the LORD said to her, "I will multiply your descendants exceedingly, so that they shall not be counted for multitude."
Is it within the powers of an ordinary angel to multiply somebody's descendants?
NKJV Gen 22:11 But the Angel of the LORD called to him from heaven and said, "Abraham, Abraham!" So he said, "Here I am."
Gen 22:12 And He said, "Do not lay your hand on the lad, or do anything to him; for now I know that you fear God, since you have not withheld your son, your only son, from Me."
The action of Abraham in not withholding his son was to God, not an ordinary angel.
NKJV Exo 3:2 And the Angel of the LORD appeared to him in a flame of fire from the midst of a bush. So he looked, and behold, the bush was burning with fire, but the bush was not consumed.
Exo 3:3 Then Moses said, "I will now turn aside and see this great sight, why the bush does not burn."
Exo 3:4 So when the LORD saw that he turned aside to look, God called to him from the midst of the bush and said, "Moses, Moses!" And he said, "Here I am."
Unless one claim that both an angel and God Himself were in the burning bush, the Angel of the Lord must refer to somebody possessing deity/