My fear is that some managers take this as a sign they need to think about replacing someone - I'd be really careful about taking this option unless I had a really great personal relationship with my manager.
If ever there was an indication that you should be courageous and do something uncomfortable, it's when you are afraid of being honest.
In this case it is a win-win even if you lose your job. If you are a)burnt out, and b)have a boss that doesn't recognize the healthy and happy employees are more productive and valuable than starting over from scratch with a new hire...then you not only are you just speeding up the inevitable departure and moving quicker to a healthier and happier place, but there is also a decent chance you are burnt out partially because you have a boss that doesn't belong in a position of managing others.
A personal relationship is part of the necessary context, but all things considered it is usually a small part.
Managers at most shops are valued by the company for their ability to build and maintain a functional team. If they have high attrition and struggle to replace people, they will get dinged, miss out on bonuses, and eventually be replaced themselves if the problem persists. Conversely, if they are churning through people and skimming off the cream to keep, no one is going to bat an eye at the number of people they shitcan or why they did it.
The relative value of having the conversation vs. not has to be considered in that context. Do you need this job to survive? Are you responsible for others' survival as well? What's the market like for people in your line of work? How is the company doing? The team? How's your manager's stock of political capital? What about the next-level manager's? Have you been doing great work (and do people know it)? Are you paid above or below market? And sure, to some extent, it matters what sort of manager you have. Some are biased toward churn, others toward retention. But the primary deciding factor here is whether your boss is going to be better off finding a way to keep you, or finding a way to replace you.
In 2015, if you are a computer programmer near San Francisco, it will almost certainly be better for your boss to find a way to keep you. The labor market in that region and sector is tight, so finding even minimally functional replacements is difficult. Unless you're an abject festering sore on the company's bottom line, you're likely to find sympathy, cooperation, and ultimately a genuine retention effort. If it were 2001? Not so much... even if you had the exact same boss. When there are legit superstars sitting on the beach desperate for any kind of work at any kind of pay, your value to the company is likely to be negligible, and at that point the only difference between a kindhearted manager and a bastard will be an offer to forget the whole conversation ever happened.
Consider the context and let that be your guide. (Good) managers are always thinking about replacing people -- not necessarily because they want to or think it's easy, but because they know they may have no choice. They have a pretty good idea of what they're willing to do to keep each member of their team given the company and market context, and what they can realistically hope to do given company policy. You should have a pretty good idea what they'd be willing to do to keep you, too. In some cases, that will be nearly anything; in others, it will be absolutely nothing.
There's no simple answer here, because the relative value of replacing and retaining people is so context-dependent.
If ever there was an indication that you should be courageous and do something uncomfortable, it's when you are afraid of being honest.
In this case it is a win-win even if you lose your job. If you are a)burnt out, and b)have a boss that doesn't recognize the healthy and happy employees are more productive and valuable than starting over from scratch with a new hire...then you not only are you just speeding up the inevitable departure and moving quicker to a healthier and happier place, but there is also a decent chance you are burnt out partially because you have a boss that doesn't belong in a position of managing others.