Push through sizers can work for PCPs, but would be ill advised for springers. It is also a matter of degree. If the sized pellet head diameter still engages the lands then so will the skirt. The skirt will just have to "blow open" fully on firing. To some degree that happens with probe loaded pellets, even when the barrel is sizing the skirt down on loading.
A pellet head is sized down so far that it rattles down the bore, it is likely going to shoot poorly. If the skirt is also that loose then it may not build enough back pressure for the skirt to "blow open" and engage the rifling properly.
A springer needs the larger skirt diameter to resist initial travel so that air pressure can build to optimal levels before the pellet starts accelerating. A loose pellet in a springer causes the piston to slam, almost like dry firing. So, sizing the head and skirt to the same diameter could be OK, if the skirt was not too small. But then, the head would be large enough to make it hard to load directly into the breech cone. Something that a probe loading PCP would hardly notice. This is not likely to occur, unless you are sizing .22 pellets down to use in a .20 .
