I assume by "ambiguous" you mean that the sentence could be interpreted as either:
If Bobby buys a pencil, (buys) an eraser, and (buys) a pad of paper, then he can write his essay.
If Bobby buys a pencil, (then buys) an eraser, and (then buys) a pad of paper, then he can write his essay.
But it's actually not ambiguous at all. "Then he..." cannot be interpreted as an item in the list, and since you say "and a pad of paper" instead of "and then a pad of paper", there is no implied sequence in which he must buy the items.
If you're just asking whether there's any need to change a comma to some other punctuation mark when multiple commas with different uses appear in the same sentence, the answer is also, generally speaking, no. The only time you'll see a comma turned to a semicolon in a list is when some of the items contain commas themselves:
He bought a car, which was red; two houses, both blue; and a diamond ring.