Cooper Bussmann writes that their Edison-base mini breakers aren't for inductive loads. I don't know too much about electricity. What does "inductive" mean?
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The simple answer is: Don't risk it and get ones that are rated for inductive loads. Here's the relevant Wikipedia article on power factor. Basically you have electrical impedance which consists of electrical resistance (which is opposition to movement of current created by resistors) and reactance (which is opposition to movement of current by all kinds of coils and by capacitors). In DC systems, the reactance is zero.
Actual reactance depends very much on the circuit itself and it can be zero and then we say that the circuit is resistive, it can be greater than zero and we say that the circuit is inductive and if it's lower than zero, we say that circuit is capacitive. By adding capacitors to inductive circuit we can make it less inductive, resistive and, if we add enough capacitors, capacitive. Same goes for other way around. If we add enough coils to capacitive circuit in the end we can get inductive circuit.
The problem here is that it's not uncommon to find device that doesn't provide enough data to easily determine if it's capacitive or inductive, what its power factor is and it can be difficult even when all that is known to calculate if the total load on the circuit breaker is resistive, capacitive or inductive. Another point is that the circuit-breakers linked don't provide (or at least I can't find) enough information to determine when an inductive load is too inductive for them.
So to be safe, just get circuit-breakers that can break an inductive load.
It means things that consist mainly of an electric motor, or have a transformer.
Things that are OK:
Things that are not OK:
If one tries to use switch to interrupt current through an inductive load, the electrons will do whatever they have to do to keep flowing for a little while. If they have to jump through the air between the switch contacts, that's what they'll do. If the electrons have to work hard to keep flowing, they'll slow down pretty quickly, but they don't stop instantly.
If one has a circuit with two thousand of watts of light bulbs and a small 5W induction motor fan, the current flowing through the fan won't want to stop instantly, but the light bulbs will provide a pretty decent path for it. A little current may try to jump the switch, but not enough to do any damage.
On the other hand, suppose one plugs in a device that acts like a pure 10mH inductor in parallel with a one-watt light bulb. The inductor would draw tens of amps, and the light bulb, 10mA. If the breaker tries to open at a point when the inductor was drawing 40 amps, then 40 amps would have to keep flowing, at least for a little while. A one-watt light bulb isn't going to let 40 amps flow through very easily; the switch is apt to be a much easier path.
The big concern with the breaker is not to use it to interrupt loads which are primarily inductive. If a load is roughly half-inductive and half-resistive, the voltage required for the current that was flowing through the inductor to instead flow through the resistor will be roughly the amount that was required to push that same amount of current through when the circuit was powered on, i.e. the supply voltage.
Note, btw, that a breaker will be able to interrupt a combination of an 5A inductive load and a 15A resistive load far more easily than it could interrupt a 5A inductive load with no resistive load. If a breaker will only be opening in case of overload condition, a 15A breaker might reasonably-safely guard a 5A inductive load, if one could be reasonably certain that any other loads would be resistive. If there's a reason for the breaker to trip, that would mean there was enough resistive load to absorb the energy; if there isn't enough resistive load, the breaker shouldn't trip. I wouldn't want to rely upon things working so smoothly (e.g. someone might use some other switch to disconnect a big resistive load just as the breaker is tripping) but they should mostly be okay.