getting back to the OP, "can someone be full of the Holy Spirit and yet not a Christian".
Good question, because filling and being FULL of the Spirit is a difference.
#1. it's not the person decision to be "Full", it's God's decision to put you into his body.
#2. filling with the Spirit have nothing to do with salvation, (BEING FULL) so yes, a non Christian can be filled with the Spirit. for we have scripture of that. Exodus 31:1 "And the LORD spake unto Moses, saying, See, I have called by name Bezaleel the son of Uri, the son of Hur, of the tribe of Judah: And I have filled him with the spirit of God, in wisdom, and in understanding, and in knowledge, and in all manner of workmanship". and there are many more OT scripture like this. but in John 7:38 & 39 "He that believeth on me, as the scripture hath said, out of his belly shall flow rivers of living water. (But this spake he of the Spirit, which they that believe on him should receive: for the Holy Ghost was not yet given; because that Jesus was not yet glorified.)
#3. in the case with Capt Cornelius. he was filled, or full of the Spirit. and was not "CALLED" a Christian yet, and he was filled before he was water baptized. but was he "FULL" of the spirit like our brother Stephen? I say yes, because of this verse Acts 10:4 "And when he looked on him, he was afraid, and said, What is it, Lord? And he said unto him, Thy prayers and thine alms are come up for a memorial before God".
peace in Christ Yeshua.