Well, technically, yes as it is hollow but I not sure that the "nut" (or whatever you call the threaded end of the skewer) would fit inside it, but it might do as it is not a thick walled piece of tube that the tool is made from. The one I used was double-sided with a Shimano tool on the other end so the tool is about 40mm wide.
What is the advantage of keeping the skewer in the hub when you loosen the lock ring? Apart from not losing the springs - been there, done that...
in some cassette hubs the RH bearing seal is just behind the lockring. This means that the tool may only protrude about 1mm (or less) through the lockring. In this case simply stopping the tool from slipping out as you swing on it is a good thing. Installing the skewer (san springs) is a good way of achieving this.
Some tools have a centre pin (~5mm dia) that goes into a standard 10mm hollow axle. This helps the tool to keep located, but doesn't prevent slippage as well as a QR skewer.
Tools with the pin also won't work with solid axles, and are of little value with through-axles. However they are not even much cop with some QR hubs; a few have push-on adaptors and these don't always support the tool properly. The outcome is often that the pin gates slightly bent and can then get stuck inside the next hub they are used in.
FWIW the current campag tool requires that you use a big washer between it and the QR skewer, if you want to hold it against the hub, because the hole in the middle of the tool is big enough to let a BB spindle through too.
If you want to use any tool with a hexagonal base, a deep pattern 1/2" drive socket is the thing; this will accommodate the QR skewer nut too.
You can clamp the hexagon in a bench vice, and with cassette lockrings this is usually OK, but it is a bad habit to get into; with freewheels they are often so well stuck that the bench vice itself make break; the forces on the jaws can easily get to well over one tonne if the freewheel is tight and the flats on the tool are small. It is a much better idea to mount a 1/2" square drive tool of some kind in the vice , such that it occupies the full width of the jaws. This will impose much lower stresses on the bench vice.
Obviously if you are using a bench vice or a double-handled tool of some kind, the tool isn't trying to cam out in the same way as it is when you have a single handle.
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