I do know that the more teeth there is on a saw blade means a more finished cut, but could that also mean a longer lasting blade since each one takes less off at a time?
Intuitively, yes, this would be the case, but the question you are asking is potentially putting the cart before the horse. One generally would not choose tooth count based on how long they want the blade to last.
Tooth count is primarily a function of the type of cut and the material you are cutting. As discussed in What is the difference between a rip-cut and a cross-cut?, crosscut blades typically have more teeth compared to rip blades. In some cases, as with table saws, you can also buy a combination blade, which has fewer teeth than a crosscut blade but more than a rip blade, and often works well enough for both types of operations.
Many other factors also influence the longevity of a blade between sharpenings, such as the hardness (e.g., steel vs. carbide, or one grade of steel or carbide vs. another) and initial sharpness of the teeth, whether the blade is properly maintained, the operating temperature, and the materials cut with the blade.
Note that higher-quality carbide-tipped blades will also have thicker carbide teeth which can be sharpened more times than those of a cheaper carbide blade.