No, He didn't when he was in His ministry
His earthly ministry was well supplied... He even had a treasurer!
That's something poor folks ain't got.
And, He was not in the town He operated from at the time He said he didn't have a place to lay His head... even so, He was very popular among the people so getting a room or someone offering Him a place to stay as He traveled was not a problem.
John 1:38,39
Then Jesus turned, and saw them following, and saith unto them, What seek ye? They said unto him, Rabbi, (which is to say, being interpreted, Master,) where dwellest thou?
He saith unto them, Come and see. They came and saw where he dwelt, and abode with him that day: for it was about the tenth hour.
Mark 2:15
And it came to pass, that, as Jesus sat at meat in His house...
Scriptures shows some of the disciples, apostles, had houses....
Matthew 8:14
And when Jesus was come into Peter's house, he saw his wife's mother laid, and sick of a fever.
Mark 1:29-33
And forthwith, when they were come out of the synagogue, they entered into the house of Simon and Andrew, with James and John.
But Simon's wife's mother lay sick of a fever, and anon they tell him of her.
And he came and took her by the hand, and lifted her up; and immediately the fever left her, and she ministered unto them.
And at even, when the sun did set, they brought unto him all that were diseased, and them that were possessed with devils.
And all the city was gathered together at the door.
Luke 4:38
And he arose out of the synagogue, and entered into Simon's house. And Simon's wife's mother was taken with a great fever; and they besought him for her.