Using pass through or Y-adapter/leads would be mentally safer, as everything is connected to right place and there is less change to confuse yourself. Electrically there is no difference.
In both cases, there can’t be any potential difference between those common leads. It might be even safer to use both C and A connectors, as there is fuse in between. Current clamps are potential free by nature, so in this case only concern that pops in to my mind is the possibility to connect higher voltage to that current clamp. –>
I live in Finland and our European plugs and sockets fit both ways, so live and neutral are basically (or at least should considerate to be) randomized every time we plug something to wall. And I am an electrician, so I measure 230/400 VAC stuff all the time. With “normal” multimeter and current clamp measuring currents is quite safe thing to do, but when adding mooshimeters ability to measure voltage at the same time, danger levels rise as now I need to remember that the clamp and leads connecting to it might have 230 volts on them.
I’m not trying to spook anyone not to do it, just saying to remember that normally potential free measuring device will end up to some voltage from your setup and will make sparks touching other parts of the thing, if there is broken insulations or some manufacturer has saved some pennies and not insulated the clamp at all.