I wonder who this is effective signaling mechanism for.
Any investor that's on the board is going to have access to data that tells the real story (or if they don't they're neglecting their fiduciary duty).
Any potential investor that's going to lead a funding round is going to do enough diligence to see what kind of financial shape they're in. And if the company doesn't have money to be increasing headcount, it'd look like they're making irresponsible hiring decisions.
For customers -- small customers are probably not doing a level of diligence that would involve going out and looking at job postings. Large enterprise customers potentially are, but when dealing with startups, they'll often have clauses in their contracts that give them access to some level of financial data to ensure the vendor they're getting into bed with isn't about to collapse (though I suppose many of them never actually enforce those clauses).
Employees pay a lot of attention to job postings, but they also pay attention to interview flow and hiring. If you have a job posting out, and no ones getting interviewed, people are going to notice pretty quickly (they're especially going to notice if someone else gets to put a req out, but the req for their dept keeps getting denied).
Definitely not suggesting the idea is wrong -- companies have certainly done far more nefarious things, just wondering who they are trying to signal to with this.