Conceptually it should increase or at least change the resultant file size. Compression depends on correlations in the image, in particular correlations in pixel values. You are changing pixel values, so you are eliminating some correlations that the compression is depending on. Saying "data which is being stored is inside the existing bits of the image" makes no sense when you are compressing. There is not only existing bits, but existing correlations you are changing.
Effectively you are adding noise in the low bits, which will always increase the size of losslessly compressed data.
Simple example: if you start off with a linear gradient in the image, with neighboring pixel values 200, 201, 202, 203, 204, 205, 206, and 207. The filter applied by PNG will take differences, which will result in (assuming you're at the start of a line) 200, 1, 1, 1, 1, 1, 1, 1. The sequence of ones compresses very well. Then you add noise in the low bits and change it to 207, 202, 205, 206, 204, 209, 210, and 210. Now the differences are: 207, -5, 3, 1, 2, 5, 4, 0. A sequence like that won't compress nearly as well as a bunch of ones.