Can someone that who has made an apparent “acceptance” of Christ and been baptized, still NOT have the Holy Spirit living in them?
Yes, of course. Someone can “appear” to follow Christ, even in baptism, and still NOT have the Holy Spirit (which means their salvation was not genuine).
All genuine occurences of salvation result in the indwelling of the Holy Spirit into the Believer. But there will be “false” converts who make every appearance of being Christian but are not.
The Bible is very clear on this matter especially in the parable of the “wheat and tares”:
Matthew 13:24-30 Another parable He put forth to them, saying: “The kingdom of heaven is like a man who sowed good seed in his field; but while men slept, his enemy came and sowed tares among the wheat and went his way. But when the grain had sprouted and produced a crop, then the tares also appeared. So the servants of the owner came and said to him, ‘Sir, did you not sow good seed in your field? How then does it have tares?’ He said to them, ‘An enemy has done this.’ The servants said to him, ‘Do you want us then to go and gather them up?’ But he said, ‘No, lest while you gather up the tares you also uproot the wheat with them. Let both grow together until the harvest, and at the time of harvest I will say to the reapers, “First gather together the tares and bind them in bundles to burn them, but gather the wheat into my barn.” ’ ” (NKJV)
To understand this parable, you need to understand what a tare is. A tare is a weed that looks exactly like a wheat plant in its early stages of growth, and only becomes recognizable as a “weed” when it ripened.
The tare would be intermingled with real wheat and rob the wheat of nutrients and water. By the time the tare became discernible from real wheat, it was too late. To try and uproot the tare would uproot the wheat as well. The only choice was to let the tare grow with the wheat, and then separate them at the time of harvest.
There will always be those who “appear” to be Christians who are not:
Matthew 7:21 “Not everyone who says to Me, ‘Lord, Lord,’ shall enter the kingdom of heaven, but he who does the will of My Father in heaven. (NKJV)
Jesus goes on to explain the parable (Matt 7:36-43) and tells us the God will separate the wheat and tares at the “end of the age”. The wheat receives eternal life, and the tares are cast in the “furnace of fire”.
Can a person be baptized and not indwelled with the Holy Spirit. Of course. There is no magic in being immersed under water. The Holy Spirit is neither obligated nor forced to indwell a person simply because a physical act has occurred.
As well, there is no doubt a person can “accept” Christ in some sort of external action and still not be truly saved. It will happen more often in an environment where the Gospel is presented as a “Jesus will improve your life” sales pitch rather than a “Jesus will save you from the coming judgment” reality check.
So to answer your question, YES, a person can APPEAR to be a Christian by “accepting Christ” and being baptized, and NOT be indwelled by the Holy Spirit.
On the other hand, a person who has GENUINELY turned to Christ in repentant, obedient belief is of course filled, sealed and guaranteed salvation through the indwelling of the Holy Spirit:
2 Corinthians 1:21-22 Now He who establishes us with you in Christ and has anointed us is God, who also has sealed us and given us the Spirit in our hearts as a guarantee. (NKJV; emphasis mine)