SMPS: Current Mode Instability (aka “sub-harmonic oscillation”) - Can we ignore it?
I'd consider potential negative effects of oscillation:


EMI. Do you need to pass EMC tests? Will there be undesirable audible noise due to magentostriction? Is the EMI likely to disrupt nearby circuits?
Ageing. If you were charging a battery I'd be concerned about localised heating and non-ideal chemistry effects. With a capacitor these issues are negligible.
Instability. Are the oscillations bounded? That is, what is the frequency response of the control loop and what's your margin for stability? As long as you have a healthy margin from where the oscillations become self-perpetuating, there's no stability issue.


As long as these issues are manageable, I can't see from what you've posted, that there'd be any issues. A PWM (bang-bang) charger, for example, would have much more significant oscillations in current, and they can be made acceptable.