With all the baseball references in The Old Man and the Sea, would I be "off base" to search for a nine inning structure to this book?
You might be “on base” with this; it is an interesting idea. Historically speaking, going by references to Joe DiMaggio, scholars suppose that the novel is set in mid-September 1950. This was DiMaggio's next to last year so there is a direct parallel between the old man and DiMaggio, both in the twilight of their careers. If there is not a nine-inning structure to The Old Man and the Sea, there might be a parallel with DiMaggio's career. In the prior season, 1949, DiMaggio missed half of the year with a heel injury. So, 1950 was necessarily a comeback season, just as Santiago was looking to come back from an 84-day slump. It was also around this time, mid-September 1950, that the Yankees won their 85th game.
There is plenty of evidence to suggest a thematic and/or structural trace of baseball in this novel. Early in the novel, Santiago carries the mast up the beach like a batter moves from the dugout (hut) to the plate/field (sea).
Structurally speaking, the old man is at sea for three days. You could at least arbitrarily if not somehow systematically divide each of the three days into three innings. The “three factor” could also be used to show three strikes or three outs of an inning. Or, maybe you could think about all three (strikes, outs, innings) as well as the entire novel being a parallel of a baseball season (or the parallel between DiMaggio's seasons 1949-1950 which include his injury and his comeback).
It all depends on the angel you're going for. A nine-inning structure could be workable, but you'd want to consider if those nine divisions are chronological or thematic. My advice would be to list all of the baseball references and see which structure or combination of structures emerge. Then ask questions like: Is the structure a game, an inning, a season, an at bat, or some combination of these? Does Santiago function as a pitcher, a batter, an entire team? Or is it deeper than that: Santiago is not only battling the fish, he is battling his age. In that sense, he is battling himself. For example, is it the older Santiago pitching to the younger Santiago, relying on “tricks” to compensate for his waning strength?
The nine-inning structure might work, but stay open to other baseball-themed structures because there may be more than one. There are also more subtle baseball references, which may not have been intended by Hemingway (however, interpretation is in the hands of the reader). The "lions" that Santiago dreams about and which are mentioned in the last sentence of the book could be a reference to the Detroit "Tigers" who were battling the Yankees for first place at this time: mid-September 1950. This may be a "stretch" (more baseball puns) but since the mast has been compared to Christ's cross and DiMaggio's bat, exhaust all potential symbols to see which ones contribute to a baseball structure and, just as importantly, any structural interpretation should shed informative or even a new light on the novel.