A good inverter will be able to sink reactive power as well as source it.
This is why, for instance, a modified square wave inverter has that flat
spot at zero volts in its PWM duty cycle. It's basically a short circuit
at that time to the AC output.
In a sinewave inverter, the output impedance ~should be~ low for either the
goes-inta' or the goes-outa direction of current.
If an inverter is making AC and gets connected to another AC source, like
the grid or a generator, then it's called "backfeed", which is sometimes
hard to protect from, but again, a good inverter will have "backfeed protection"
and shut off when it sees high current at the wrong time in the AC cycle.
Spikes can be helped by different methods like MOVs and stuff, if that's what
you're talking about.
boB