Usually, no. SD cards draw very little power compared with the camera itself, so in normal use you should not see a meaningful battery-life difference just from card speed class or capacity. A 32GB card should not drain the battery faster than an 8GB card, and a Class 10 card is not inherently a major battery drain compared with a Class 4 card.

That said, some users do notice differences between specific cards. This is more likely due to the card’s brand, controller design, or overall quality than its stated speed class or size. Poorer-quality card electronics can be less efficient and may have a small effect, especially during heavy continuous writing such as video recording.

So the practical answer is: capacity and speed rating alone generally should not matter much, but individual cards can vary slightly in power use depending on their internal circuitry and quality.