You will not be able to detect the global change you describe because the libraries will need to be normalized for sequencing depth. As ATpoint points out, ChIP is also noisy, the background signal may change rep to rep and not be indicative of changes in target protein abundance.
So, for example you may pull down half as much DNA in your treatment sample. This may be due to lower target abundance, but could also be due to chromatin shearing differences or efficiency of any intermediate step (IP, reverse x-link, DNA purification...). There are protocols that suggest exogenous spike-ins can help normalize for global changes, but these come with issues of their own that need to be considered in context of your specific experimental design.
Furthermore, even if half as much DNA is indicative of lower target abundance and you use this as input and prep libraries and sequence them while keeping this relative input amount, there's still variation introduced with the number of sequencing reads produced. First, if you sequence half as much DNA you might expect half as many reads, then you map these and present them, showing on average, half the signal across the genome. I don't think any reviewers will accept this as valid. Furthermore, the read yield will also likely vary due to various factors, including clustering efficiency, pipetting error, etc. So usually you will need to normalize to the total number of reads, removing the whole point of starting with half as much DNA in the first place.
Additionally, during the library prep, if input amounts are vastly different that can introduce noticeable biases in the libraries, especially during the PCR step.
So I think if you have the ability, you should equalize your input DNA amounts, then hopefully differences in library composition are indicative of the IP'd DNA and not of your library prep method.
I hope that's relatively clear and helpful.