I've tried this on some Original Xbox's that I've worked on in the past. I found that the forward voltage of the 1N4148 is too much for a CR2032 and the Xbox didn't have enough current to keep the time. I found that AA's work with the 1N4148 for this purpose. You could also bypass the need for a diode at all by using lithium rechargeable doubles A's - or a LIR2032. Anyways, I made a video on this exact subject a while ago. If you can't identify the clock cap - you can always identify it by it's PCB designation (which is C7G3)
Been charging Nicad, Li-ION, and LiPo batteries without their protection circuits, with my bench power supply for over two years. As long as the battery isn't over-volted, you'll be fine.
Well, if you want to do that - then that's fine. But recommending others to do that is dangerous. It's not just overvoltage but over charging when full. You are supposed to stop charging when it full, which just throwing one in an xbox, where it will be getting power when ever it's plugged in is a very very bad and dangerous idea. Worked for you, in a setting where you can disconnect the power and whats safe (especially in a device that delivers constant power) are different things. http://www.digikey.co.uk/en/articles/techzone/2012/sep/a-designers-guide-to-lithium-battery-charging
As a general rule of thumb, you're definitely right. However, all or most rechargeable battery A/C adapters are "dumb" adapters. Many laptops, for instance, will keep charging a battery non-stop unless it's unplugged. Likewise with rechargeable battery A/C adapters. In my experience you have to actually pay more for a "Smart" adapter that will shut off power when the battery is done charging. The only issue with giving a rechargeable battery constant current; is the fact that you'll run down the battery to the point where it won't hold a charge pretty quickly if you use a "dumb" adapter. Also given the fact that the Xbox feeds the 1 Farad cap only 2.5ish volts; and since the charging current of a LIR2032 is supposed to be 4.2 volts, 20mA... you'll be fine - it's not dangerous in anyway. And for conversations sake - let's the worst happened, and the battery exploded. It'll definitely catch fire, but not for long - and any "explosion" would easily be contained inside the Xbox.
All lithium chargers are "smart chargers" in my experience as thats how they need to be charged and the circuity to do it is pretty minimal. It's also why all standard Nicad and nimh chargers say not to use lithiums in them. Lithium go into a trickle charging mode that's topped up constantly as it drops below a threshold voltage. This is actually better for lithium cells anyway (unlike nimh and nicad). They don't just keep charging when its full though. Nicad and nimh you can quite correct though that cheap chargers are just constant low current. But again, my main issue isnt that its probably safe most of the time. It's recommending it to people who will blindly follow it, because it's on the Internet. They may even see your advice then apply it to a different circuit, that is more dangerous. Etc
I think we're both making good points, and your right - people on the internet tend to take things too literally. But I see no reason, in this case specifically, why this would be dangerous. I also don't think that people would apply what I'm saying here to batteries in general because were not talking about batteries in general. Just as a replacement for the 1F cap in an Xbox.