More importantly, will the employer think that you are underpaid if you don't volunteer the information? Imagine dating someone and asking them "Have you ever been arrested before?", and they answer "I would rather not say".
It is very common for people to believe that an employer is just going to say, "Oooh, they made X. Let's offer them X + 15% even though their expectation is X + 40%". While I am sure that it happens in mom and pop operations that don't know how to run a business, think about this from a large company's perspective:
1) The hiring manager needs to fill a role. I promise you that this is their priority, not nickel and diming potential hires.
2) The company invests resources into testing/interviewing, etc., and a needed hire represents lost opportunity. They're not going to blow up the deal even though the expectations are in line, because the ask is a few 10's of percent over what they were making before
3) It makes sense for the company to pay satisfactorily, since they don't want the employee becoming disgruntled when they find out they're paid less than their coworkers, or that they could get what they want somewhere else.
4) Who's watching the bottom line so closely? Unless a very myopic owner of the company is doing the hiring, HR wants to hire people (it's actually their KPI, not how much below market they manage to underpay new hires), and managers and team members want the additional heft.