Well, put it this way. Power supplies have been made with low-Q inductors for ages. Yellow powdered iron cores for example. Laminated iron going back even further (a number of PDP-11s, etc. were made with somewhat rudimentary SMPS, bipolar switch and laminated choke, low 10s kHz). Low Q is not strictly a barrier to high efficiency. The tradeoff is, you need to make reactive power small in relation to DC power, i.e. large inductance / low current ripple fraction.
There are only two effects to nearby copper:
1. Reduced Q of the inductor itself
2. Induced voltage in said copper
#2 we can discard easily by designing it with solid ground plane, so that the induced voltage is mostly shorted out and doesn't wind its way into signals, or common mode in nearby connectors, etc.
That leaves #1, and for typical leakage, like say, well heck let's even go worst-case and say it's an air-core inductor of modest aspect ratio (say 1:2 to 2:1), solenoidal design, and resting flush on the board. The coupling factor (which because of the shorting plane, is also basically the inductance reduction factor) will be in the 0.2, 0.3 range for such an arrangement, maybe up to 0.5 for a squat inductor with axis normal to the plane. Easily under 0.1 for some height above the board, and easily under 0.05 for anything with a core (even if the air gap is placed directly against the plane, cooking it by fringing field). "Shielded" types may be in the 1% range; I think I would be surprised if anything off-the-shelf and not specifically contained (like with a flux (shorting) band around the core) would do much better than 1%; this is because k ~ k_aircore / mu_eff, and mu_eff ~ 50 for typical inductors.
Even if the plane were a perfectly matched resistor, exactly absorbing the incident field and neither reflecting nor passing it, the coil's Q due to plane effect won't be less than 1/k. And for the real case, where copper is a pretty good reflector of field (even such low impedances as in SMPS coils, fringing field, etc.), the Q will be higher while L_loaded sees a stronger reduction instead. (That is, as you vary R_load of a nonideal transformer, for R --> infty, you get L = Lm; for R --> 0, you get L = LL; for inbetween values, you get some mix of L (intermediate between these extremes) and reflected R, as the total impedance traces an arc on the Smith chart.)
So the verdict is:
It depends.
Namely, it's far more important in high-ripple, high-efficiency designs; peak current mode control, DCM, BCM, or quasi- or fully resonant types, are typical examples. These will also be applications where litz wire on gapped ferrite are preferable over solid or edgewound wire on powder or composite cores. Q of hundreds (thousands, even?) might be demanded. Trying to use an unshielded inductor over solid plane, may unduly affect the Q, and efficiency is lost, operating temp rises, etc.
Low-ripple, high-inductance, average current mode, COT, etc. types can deal with lower Q, and hence the lossier materials and constructions are acceptable, and plane induction is less important.
Tim
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