Parallel charging LiPo packs has become very common in the RC hobby. Granted, there is not a lot of empirical evidence about how good or bad this is. Only the fact is that a lot of people do this on a daily basis.
Personally I have been parallel charging 6s LiPo packs for 2 years now with good results. I have some budget packs that are over 100 cycles, so in that regard, I am happy with the life I got out of the pack.
My parallel charging routine was not very stringent. I likely never charged packs with over a 0.25V/cell difference during this time. I think in the future I will be more careful about the voltage of the packs. My recommendation would be to stay under 0.1V/cell difference.
The problem with parallel charging is that it is quiet easy to make a mistake, and connect packs of dissimilar voltages. So if you are going to do this, I would always double check your pack voltages before connecting.
A very good resource on parallel charging can be found on the Tjin Tech site. This is a very thorough examination IMO. If you scroll to the bottom it also addresses the potential surge currents when connecting the packs, and also includes experimental measurement of current that is released at the initial connection.
You want a power supply that reasonably regulates voltage and can put out 1/2 killowatt at 12 V. That's going to cost some money one way or another. If you add to that current limiting (current regulation) and adjustable voltage, it will cost even more money. These things take some engineering to do well, safely, with regulatory approval, and the volume won't be that high. That all means a commercial product that does all that will cost real money.
If you are going to draw 40 A, then maybe you should be using a higher voltage, like 24 or 48 V. 40 A is going to require thick cable and will otherwise create hassles. You can probably deliver and use 10 A at 48 V more efficiently than 40 A at 12 V. Note that the issue around efficiency isn't so much wasting the power, but dealing with the heat the wasted power causes. A 90% efficient 480 W supply will cause about 50 W of heat.
As for your current limiting spec, it seems you don't really want current limiting at all, but rather overcurrent tripping. That is also sometimes called a electronics fuse. Fortunately, unlike with current limiting, overcurrent tripping can be added separately after a canned supply. For sake of keeping a common ground for measurements and the like, I'd probably use a high side current sense resistor, with something like a INA169 to bring the signal down to the ground reference.
I'm am doing a project right now that includes two electronic fuses. A microcontroller is watching the current sense signal every 10-20 µs in a periodic interrupt. If the current is above the trip point, a counter is incremented. If below, the counter is decremented unless it is already zero. If the counter reaches a particular level, which means the current has been high for some pre-determined amount of time, then the output is shut off for two seconds.
You need to set the trip time long enough to allow for inrush as power on. Or, you apply the algorithm differently at power on. Right now I am using a flat 2 ms for one supply and 750 µs on the other, but that one does a soft start during which the fuse is handled differently.
20 ms seems like a long time, but is still faster than most real fuses take to blow. I'd look at the current profile at power on, and set the fuse a little longer than that takes.
You don't need extra fast switches after the current sense resistor. At most, they will switch once every two seconds, or whatever you set the fuse recovery time to. You don't want to make the switching time so slow that significant heat is dissipated in one transition, but a few µs as apposed to the more normal few 10s of ns should be fine.
Best Answer
With just the batteries? Nope. Current can only flow if the loop is closed.
BUT!
With LiPo batteries there is often a control board, they will at least still use a tiny amount of power (in the order of micro amperes usually). Some more advanced technologies can actually actively balance cells while in use or while charging, Linear had a nice chip that does that. In such a case a little while after you switch it off, it may keep currents flowing around between the batteries to balance them for a tiny while after. But those packs will be very rare.
So simply put: If there's electronics in there, anything could be happening, if there isn't, then loop broken means no current anywhere, ever. Although with LiPo it's very smart to have electronics at least for per-cell protection.
(Except for a battery's inherent self-discharge, but that's a current that flows inside each cell, so that still doesn't affect other cells in the chain and that is extremely low for Lithium types.)