Johnson joined the Black Cats on Friday for a fee believed to be around £10m, but wouldn't have been able to make his debut against Reading had their Saturday match gone ahead.
"Adam, with playing for England, his fitness is fine and a lot more advanced than Steven Fletcher," said O'Neill.
"In fairness, Adam wanted to get things sorted on Friday, but the timing for Saturday just beat us.
"I think for him, it would be a great opportunity. He will be playing."
League Two's Morecambe progressed to the second round with a 2-1 win over Championship side Blackpool.