Can a capacitor damage an Arduino?
Edit: Just to get this in proper format for closing, I would note that you already had this 99% figured out. After adding the resistor, the pin is protected from anything and everything downstream; the only consideration is the effect that a limited current supply will have on the downstream devices. Additionally, with the recommended bypass capacitor on the Arduino's power pins, an additional capacitor is probably unnecessary.

The math behind the OP's values is as follows:

$$E = I \cdot R$$
$$R = \frac{E}{I}$$
$$R = \frac{5V}{0.0278A\ max} = 180 \Omega$$
$$E = I \cdot R$$
$$E = 0.001A * 180\Omega = 0.18V\ drop\ across\ R$$