What are the effects of adding winglets to an aircraft not designed with winglets originally?
Aircraft wings are designed for specific weight and cruise speed. When later the manufacturer wants to create a new variant with higher maximum weight, it should get longer wings for optimal efficiency. However, redesigning the wing is a lot of work, because extending the wing means the root bending moment increases, which requires stronger spar, which means heavier and all the calculations have to be redone.

Here is where winglets get useful. They increase the effective wingspan, but while they are somewhat less efficient than extending the wing, they also cause lower increase of the root bending moment. Often, this smaller increase fits in the original extra margin, so winglets can be simply bolted on without having to redesign the wing, making the process much cheaper. 

That's why we often see winglets on next generation of anything and rarely on the first generation. On first generation, they are designing the wing from scratch anyway, so they just make it appropriate length for minimum drag.

The main reason to use winglets from the start is if the emerging design just slightly exceeds some size category for airport gates. Then it makes sense to reduce the span to fit and add winglets so the aircraft can be used at smaller—and therefore cheaper and more common—gates.

You can read how winglets work in Is a winglet better than an equal span extension?.