The primary thing that can affect size are images. If the original images are jpgs, you can decrease their storage size by compression. But the greater the compression, the greater the images quality goes down.
then, with any image, the higher the resolution, the greater the storage size. Is you double the resolution, the storage size goes up 4x. Where people often go wrong is using an image larger than they need. For example, if you need a resolution of 300 poi, a 2" image is 600 pixels wide. If you take an image from a phone and place it directly into the document, it is likely to have a width of 4000-5000 pixels. That's a lot more than you need and significantly increases the size of the document.
but, to your question of the search ability to affect storage size, we'll, that's pretty irrelevant.
Personally, I'd say, firstly, reducing file size may affect FUTURE work on search ability very much. Because OCR depends on good quality originals, and reducing size is always reducing quality. Secondly, OCR can replace images with text, so it may hugely reduce file size, finishing the job. Check OCR options carefully.