When asked about where I wanted to be in my career by my boss (boss' boss actually), I was honest about having my resume out there and looking for other opportunities outside my current company. Now, I've heard from other sources a promotion that was possible in my future has been basically pulled.
Honesty is not a good policy. Keep lying.
Everyone says they want the truth, but if you are told you're not doing meaningful work, the justification for your job is vanity metrics, and the guy with less experience than you who does terrible work makes more money than you, how happy would you be?
If you told management, you're using the position and any promotion as a jumping off area for a newer better job at a different company, how happy would management be?
If you're shopping around this can mean your employer has already refused to invest in you, no?
Obviously you are omitting the myriad of cases that an employer would like to invest in you but can't (yet) from your statement. Plenty of things like a lack of funding, individual ability, market timing, etc. prevents them from investing in you.
If I was waiting for the cash flow to move someone from A to B, and was working diligently to do so, to then have them state they are looking elsewhere for the B position, I would clearly re-evaluate my candidate selection as they may be gone by the time I get the opportunity to promote.