Back with a few empirical measurements:
I connected an 1A analog ammeter at the XL6007 input, to see how much current the converter draws with the capacitors connected at the other end. Previously, I used this method to see how much current the cold tube filament draws. For a split second I could just see the needle jump, and this was roughly consistent with the theoretical expectation when I used different—yes, beefy 2W ceramic—current limiting resistors).
The needle jumped to about 0.5A, nowhere near 1A (the maximum).
I then tried the same approach using 100Ω resistors instead. Theretically, we should expect a lowpass filter at 1.5Hz but a voltage drop of 2V (which would still be acceptable for the circuit in question).
Interestingly, with 100Ω, I got a negligible (<0.1V) drop at the rails, nowhere near the theoretical 2V, and the inrush current draw at the input was much lower, about 0.2A.
I then tried measuring the inrush current at the XL6007 output, i.e. the 100Ω resistor. Unsurpisingly, it did not register at all in the ammeter, as the voltage drop was negligible.
To ensure that the rough ammeter measurements were not way off (e.g. the needle did not have enough time to jump higher), I used a normal (i.e. not slow blow) 0.5A fuse at the XL6007 input. The fuse did not blow.
Given the above, I can only assume that:
- The XL6007 has excellent voltage regulation at the output, which is not affected by the series resistor at its output as much as we would expect.
- The XL6007 internal slow start circuit is efficient in limiting the inrush current to the presence of capacitors at its output. Besides, the datasheet implementation of XL6007 as a double SEPIC (which these Chinese modules are) has 220μF capacitors at the output, but it seems that its ability goes far beyond that.