If the question is "What did you PAY for it?", then just tell the truth. That has no bearing on the actual value if it were to get written off. Vehicles do depreciate/appreciate differently, and the condition you bought it in could change after you've invested some time/money. On the other hand, if the question is "What is the value?", then you have to be more careful to determine whether this means the insured value, or really the purchase price. In either case, it sounds like you don't care what they will pay out, so just go with the purchase price. If they were somehow able to find out what you actually paid (which seems unlikely), then you won't be caught in a lie which will definitely void your policy.
NFP estimated $428/yr for my Hawk pending appraisal for vintage insurance, with the assumption it was mostly stock. I have to imagine that Hawks were valued at less than $2000 at the time, but I don't know for sure. The appraisal valued a stock one at $4000, then added all my upgrades which came out to a total of $13,000 and increased the final quote to $531/yr. So $100/yr premium difference on $11,000 value difference.