I think the problem you would have with your boss would be that your boss asked you 'how long will this program run', and if you told them O(1), the question you are really answering is 'what is the time complexity of this algorithm, parameterised by the number of entries, as the number of entries tends towards infinity'.
If your boss really wanted O(), then they wouldn't care that hashing one key takes a day and another a second, because they're thinking in terms of a hash with infinite entries, so the difference between a day and a second to hash is irrelevant.
If you released software that was exponential, but your QA department only ever tested small inputs, I think it would be negligent to omit to your boss and|or clients the rate at which run-time could expand.
and I think it would be a horrible manager to not care about the difference between a day and a second.
If your boss really wanted O(), then they wouldn't care that hashing one key takes a day and another a second, because they're thinking in terms of a hash with infinite entries, so the difference between a day and a second to hash is irrelevant.