"For small values of n, O(n) can be treated as if it's O(1)"
This is largely piggy-backing on the answers already posted, but may offer a different perspective.

It's revealing that the question discusses "sufficiently small values of n".  The whole point of Big-O is to describe how processing grows as a function of what's being processed.  If the data being processed stays small, it's irrelevant to discuss the Big-O, because you're not interested in the growth (which isn't happening).

Put another way, if you're going a very short distance down the street, it may be equally fast to walk, use a bicycle, or drive.  It may even be faster to walk if it would take a while to find your car keys, or if your car needs gas, etc.

For small n, use whatever's convenient.

If you're taking a cross-country trip, then you need to look at ways to optimize your driving, your gas mileage, etc.