I've done this with an old B&D 12V NiCd drill with success. Converting to external 12V works fine for NiCd and NiMH tools, since the technology is rather simple and the running voltage is actually 12 volts DC, give or take. Trying to do this with newer LiIon-powered tools is not a good idea for a couple reasons. Because of additional safety factors involved in LiIon tech, tools are almost always equipped with several safety monitors in the circuitry built into the tool. Temperature, voltage and cell balance are all measured by the tool electronics while operating. Note the number of connections a LiIon battery has between it and the tool compared to a NiCd or NiMH. Not only are the basic battery connections present (usually the two biggest connections) but several smaller ones. This is used to relay information between the cell pack and the tool in order to keep the usage of the cells within safe parameters. LiIon cells can't be discharged below a certain voltage before they become permanently damaged almost instantly. The electronics monitor the total voltage and will shut down the tool when it falls below a certain level. Cell balance also plays a critical role. With several cells in series, one or two are bound to discharge more than the rest while still keeping overall pack voltage within safe specs. If one cell drops below it's minimum spec, this won't always trigger the total voltage drop protection. Eventually this cell will become "reverse charged" by the remaining good cells. If this happens, the cell is immediately and irreversibly damaged. If a large amount of reverse current is applied, the cell can burst or vent, which can lead to sparks or fire. The electronics measure individual cell voltage or a split between groups of cells to determine if any cells drop before the rest, this shuts off the tool to save the cells and maintain safety. In LiIon chargers, this monitoring is used "in reverse" to make sure a weak cell does not become overcharged before the rest catch up, this is very critical. If a LiIon cell is charged beyond full capacity, there is a risk of cell rupture, venting and fire. Should a bad cell in series with good ones suddenly go beyond critical spec, the charging is shut down and (usually) some indicator on the charger is shown denoting a defective pack.
Cell temperature is critical in NiCd, NiMH and especially LiIon. There are temperature sensors in most packs that are used by both the charger and the tool. Charging a battery outside of temp limits (hot and cold) can damage it. There is usually a warning light or indication on the charger for this. Using the tool hard or overloading it will heat up the cells, the sensor will be used by the tool to shut off the tool until the cell cools. Putting a hot pack into the charger will put the charger into a delayed or low current mode until the cell cools. Some chargers have a fan that speeds this up.
There is also overcurrent protection in tools and/or battery packs. Some tools use this parameter more carefully than others. A drill, driver, saw, grinder or any other tool that can be accidentally or deliberately stalled will usually have some sort of active overcurrent protection, especially LiIon. Tools that are tough or impossible to stall such as impactors, lights and such might not care much of at all, or have basic protection. People complain how today's powerful LiIon tools are sometimes heavy handed in overload protection, but there's a good reason for this. I've found that Makita 18V LiIon tools have less protection than other brands, especially the white lighter duty series. One drill I have started smoking instantly when it bound up, I exchanged it thinking it was defective. Upon further investigation (I tore open the new tool for a peek inside) I found there was absolutely no provided protection, and only the two main battery terminals were used. These tools were relegated to light duty around-the-house work.
What does all my blather have to do with converting tools to run on car batteries? In the case of any LiIon tools branded "12V" there is the real risk of running the tool on a higher voltage than nominal. Since the LiIon batteries indeed push close if not slightly more than 12 volts when first taken off the charger, this is not going to be too big a deal, at least at first. Since the LiIon cells drop to 10.8 volts or so once in use, running the tool on 12+ volts continuously can likely overwork it and possibly shorten its life. The real issue is all of the expected interconnections between the LiIon pack and the tool not being in place. Few tools I know of will operate if there arent valid signals from the pack to the tool. By just connecting the main supply voltage to the tool, you leave open the cell balance, temp and other protection inputs. The electronics won't have any of this, and will prevent the tool from running. It IS possible to fool the tool by providing it with false inputs, but this can be tricky depending on how sophisticated the interlinks are. Gutting a LiIon pack and installing a voltage divider made up of resistors to trick the tool into thin king there are three (in the case of 12V LiIon) cells is not a big deal. The thermistor can just dangle around inside the hollow pack. Add a substantial fuse (at least 10 amps) in line to protect the tool. The consideration now is what will the tool do if it is used on a vehicle battery while the engine is running, and the voltage is 14+ volts...