#### Answer

No. When we do order-of-magnitude calculations, we should not be concerned about significant figures.
An order-of-magnitude calculation gives only an estimate. But this
estimate may be enough to provide you with a better grasp or understanding of a physical situation. Usually, the result of an order-of-magnitude calculation is precise within a power of 10, or within an order of magnitude. That is, the number (prefix) multiplied by the power of 10 is somewhere between 1 and 10. For example, if a length result of $10^{5}$ km were obtained, it would be expected that the exact answer was somewhere between $1\times10^{5}$ and $10\times10^{5}$. So, we should not be concerned about significant figures.