I think the 10,000 strong army would have been enough to take Helm's Deep, if things had gone to plan. After that I don't think Saruman would use that army alone to take the rest of Rohan. He would most likely have continued breeding Uruks for dear knows how long.

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Better, though difficult, the right way to go, than wrong, though easy, where the end is woe. John Bunyan - Pilgrim's Progress