Nick Rowe asks another interesting question.
In the comments I eventually disagree. If the hypothesis is true, it should apply to equity markets. But Nick can't provide a measure of price stickiness in equity markets. I for one have don't know what a "sticky" stock is. My hunch, guided by experience, is that bids and offers for stock X will react almost as quickly to news and events as those for stock Y.
But stocks are certainly more or less liquid. So you can have varying grades of liquidity without varying grades of stickiness. Thus, the two concepts aren't related.