In uncompressed form, yes - in compressed form no, not necessarily.
In compressed form content is the dominating factor as well as type of compression. The more high-frequency signal the image has (noise, details) the harder the image is to compress, so two images of the same dimension can be compressed to two different sized depending on the content.
One small image with high frequencies can become larger than a large dimension image with low frequency (blurred, noise-free etc.).
If you get an image with large size after compression you can use low-pass filtering on it (ie. here: blur it a bit).