Charging a battery project
As long as the voltage doesn't exceed the safe voltage for the battery then a precise DC supply isn't too important - depends on the battery technology/chemistry.
In fact having a lead-acid battery being charged in parallel was a common way of smoothing DC before solid-state DC-DC regulators.

But 3.7v suggests you are trying to charge a Lithium-Ion battery, this can get dangerous if you overcharge it. You really need a charger-controller IC for Li-Ion, or at the least a protected cell