Yes—this is a reasonable workflow, but it may take two parts: a resize tool plus your operating system’s scheduler.

From the answers:

• ImageMagick is a strong option for the actual resizing. It can batch-scale images well, but scheduling and “only process new files” behavior would usually be handled outside the program, such as with an OS task scheduler or a scripted workflow.
• IrfanView is a good free option on Windows. Its batch resize/resample mode is well regarded, and it offers control over resampling algorithms and sharpening, which can help maintain quality when making images smaller.
• FastStone is another free, simple alternative that can do more than just resizing.

Whichever tool you choose, pay attention to the resampling method and consider output sharpening, since downscaling often makes photos look softer.

So the practical answer is: use a batch-capable resizer like ImageMagick, IrfanView, or FastStone, and pair it with your OS scheduling tools if you want it to run periodically.