> choke coils
Covers a LOT of types, from iron shell-core to 4 turns around a soda-straw.
> this would be two EI chokes
Jam them in how ever fits.
Except right at a gap, the field is 99.9+ in the iron, does not go through air.
EI *chokes* are usually gapped; don't butt the gaps against each other (this would be difficult to do). A gap-thick space improves things a lot.
At the school we had drummers and we had harpsichordists. They needed practice rooms. Imagine a room 99.9% sound-tight, 0.1% through the door-crack. If two doors are spaced along a hallway, further than a crack-width, leakage is teeny. If we ram the doors together (there are modular practice rooms which can be moved) crack-to-crack, leakage will be higher.
JAMMING an E against another EI's gap is also bad, bridges the gap. It is nearly impossible to get enough contact/proximity to matter, you'd need a hammer.
The EI is critical. When you move to loudspeaker chokes, they are often air-core or stick-core. These will mutual very significantly. You see aircore crossover chokes mounted well apart and at right angles.
> Does the effective inductance of each increase or decrease?
Of "each" is often not as important as what the coupled signal does. In a L-C-L-C power filter, any coupling from first to second throws large ripple through to the output. In a stereo tone-filter, the bleed from one channel to the other may show as "poor" stereo separation.
Can't you breadboard? Mock it up spread-out. Test. Then flip the one choke over the other, test again. Actual trial and success/disappointment may tell and teach you more, and more memorably, than innernet chatrooms.