I believe the valve spring in my 360 are the same as the ones pictured here

Would you pull the inner spring during cam Break in?

Cam isn't very radical. Hyd cam with under .300 duration.

I don't do it. If it starts up like it should it isn't worth it.

Without knowing the exact pressures on the seats and open and coil bind clearances I wouldn't do any decision making either way
I don't remember the exact installed height for stock 360 heads but I do remember them being quite a bit shorter installed height than stock BB springs are
Don't take a chance until you get more information as far as how much pressure on the seat and opened
I use from 140 to 175 Lbs. on the seats on flat tappet cams and up to 375 lbs. open with as little as .060 from coil bind and shoot for no more than .100 from coil bind at max lift on any motor that will be shifted at or above 6000 RPM with out removing the inner springs, if yours has more pressure than that stated above I would remove them
IHTH

pull em. this is std procedure & cam failures are epidemic. Mr Murphy is always waiting.

Removing the inners doesn't prevent cam failures if you screw everything else up.

Motor has to be clean, clean, clean; lifters free in their bores; no guide to retainer(seal to retainer) interference - proper clearance at max lift; no coil bind at max lift; all internals pre-lubed; correct break in oil and/or additive package; spin distributor out of engine to make sure you have spark at the plugs; carb bowls full; get oil pressure; install intermediate shaft then install distributor and verify timing is dead on using rotor and #1 tower in distributor aligned properly and reluctor to pickup coil aligned ( or points set ); engine full of coolant; fans in front of engine; light the engine and get up to speed and break in -

Yes,

I would pull them. Less pressure is better during break in. I would also make sure the engine is ready to start and once started rev the engine from hi idle to 2000 RPM over and over and over for a few minutes to help promote spinning lifters.

Good luck with your build.