The answer to the question "What is the relationship between rna levels and protein levels" is: it varies.
I'd address this question with a thorough review of the literature. A PubMed search for mRNA protein correlation returns many results but if you look at the box titled "Titles with your search terms" and click "See more" on the right of the results page, you'll find more relevant and useful articles.
Just taking the first 3 results as an example:
Ref. 1. Delayed correlation of mRNA and protein expression in rapamycin-treated cells and a role for Ggc1 in cellular sensitivity to rapamycin.
They find that for proteins which decrease in abundance on rapamycin treatment, most of the mRNAs also decrease; but the same is not true for proteins which increase in abundance.
Ref. 2. Correlation of mRNA and protein in complex biological samples.
This is a very useful review article. First sentence: "The correlation between mRNA and protein abundances in the cell has been reported to be notoriously poor."
Ref. 3. Correlation between protein and mRNA abundance in yeast.
From the abstract. "We found that the correlation between mRNA and protein levels was insufficient to predict protein expression levels from quantitative mRNA data. Indeed, for some genes, while the mRNA levels were of the same value the protein levels varied by more than 20-fold. Conversely, invariant steady-state levels of certain proteins were observed with respective mRNA transcript levels that varied by as much as 30-fold."
Thank you for these references. I will keep them in mind when analyzing RNA seq data!