Is it possible to feel the presence of God when one worships Him?
You ask the question in the wrong way because in the realm of possibility when dealing with God, almost anything is possible. But if you ask how God made His presence know in the past, then we find:
"And they heard the sound of the LORD God walking in the garden in the cool of the day, and Adam and his wife hid themselves from the presence of the LORD God among the trees of the garden" (Genesis 3:8).
"So Moses and Aaron went from the presence of the assembly to the door of the tabernacle of meeting, and they fell on their faces. And the glory of the LORD appeared to them" (Numbers 20:6).
"So it was, when Elijah heard it, that he wrapped his face in his mantle and went out and stood in the entrance of the cave. Suddenly a voice came to him, and said, "What are you doing here, Elijah?"" (I Kings 19:13).
Physically Felt (Earthquake)
"The earth shook; The heavens also dropped rain at the presence of God; Sinai itself was moved at the presence of God, the God of Israel" (Psalms 68:8).
"Tremble, O earth, at the presence of the Lord, At the presence of the God of Jacob" (Psalms 114:7).
"The burden against Egypt. Behold, the LORD rides on a swift cloud, And will come into Egypt; The idols of Egypt will totter at His presence, And the heart of Egypt will melt in its midst" (Isaiah 19:1).
"I beheld, and indeed the fruitful land was a wilderness, And all its cities were broken down At the presence of the LORD, By His fierce anger" (Jeremiah 4:26).
These are times with God made His presence known. But God never said that His worshipers would feel His presence while they worship Him. Jesus said he would be there. "For where two or three are gathered together in My name, I am there in the midst of them" (Matthew 18:20). But it is by faith that we accept that this is true.
God doesn't use vague feelings to communicate with man. He even said not to trust feelings. "He who trusts in his own heart is a fool, but whoever walks wisely will be delivered" (Proverbs 28:26). Our faith comes from what God said. "So then faith comes by hearing, and hearing by the word of God" (Romans 10:17).
The reason ancient Israel was lead astray was because false prophets didn't offer God's Word, but their own imagination.
"And the LORD said to me, "The prophets prophesy lies in My name. I have not sent them, commanded them, nor spoken to them; they prophesy to you a false vision, divination, a worthless thing, and the deceit of their heart" (Jeremiah 14:23).
"Thus says the LORD of hosts: "Do not listen to the words of the prophets who prophesy to you. They make you worthless; They speak a vision of their own heart, not from the mouth of the LORD. They continually say to those who despise Me, 'The LORD has said, "You shall have peace"'; And to everyone who walks according to the dictates of his own heart, they say, 'No evil shall come upon you.'"" (Jeremiah 23:16-17).
"I have heard what the prophets have said who prophesy lies in My name, saying, 'I have dreamed, I have dreamed!' How long will this be in the heart of the prophets who prophesy lies? Indeed they are prophets of the deceit of their own heart" (Jeremiah 23:25-26).
It wasn't just the prophets, the people did the same. "This evil people, who refuse to hear My words, who follow the dictates of their hearts, and walk after other gods to serve them and worship them, shall be just like this sash which is profitable for nothing" (Jeremiah 13:10).
Therefore, following after your own feelings is not a guide to the truth.