I do not know what type of boiler you have, or what corrosion inhibitor you have, or much else. But...
With a Central Boiler plain steel OWB, the first year I burned off the creosote with a propane field burner, and then roughly scraped it down with a hoe and emptied out the ashes. Then I sprayed the inside with a thin coat of WD-40. Then I put a bucket over the stack and shut it down for the summer. The next year I did pretty much the same thing. The next year after that I left one inch of ashes in there and I put a rain cap on so I would not need the bucket any more. I did not do the WD-40 thing either. Last fall before the heating season, I drained the OWB water and refilled it with fresh, and treated it with corrosion inhibitor again. I also replaced the door cord and adjusted the door handle.
From the research that I have done, the creosote itself will not corrode the steel much, if at all. Neither will the ashes, as long as they are dry. The real culprit to steel is any water that gets trapped under the creosote or in the ashes. So give it a good hot burn before you shut it down and make sure it has a rain cap in summer. The pump should be fine doing nothing.