Did that quote come from the 1702 datasheet? I found this:
The maximum rated continuous output current for the...
...A minimum output capacitance of 1.0 μF is required for
small signal stability in applications that have up to
250 mA output current capability. The capacitor type
can be ceramic, tantalum or aluminum electrolytic. The
esr range on the output capacitor can range from 0Ω to
Jeenode, which uses the same regulator, uses a 100uF output capacitor. Would it be OK to use a 220uF electrolytic capacitor?
Probably. Current flows through the regulator into the output-capacitor, charging it up, when you first turn-on the power. A bigger capacitor will "suck up" more current, and this could be a problem with some regulators. Most voltage regulator chips have all kinds of built-in protection and the worst that is likely to happen is that the regulator will fail to start-up... You are not going to permanently damage the thing with a big capacitor on the output.
Does using a higher capacitor value effect efficiency for battery powered applications?
The capacitor stores energy, but it doesn't use any energy so it won't affect efficiency. Once the capacitor is charged, it's just sitting there filtering-out a little noise and preventing oscillation before it starts.
Usually the datasheet is reliable and it's ALWAYS the best place to start, but sometimes you have to do something different... Where I work we are using a regulator that we haven't used before (MIC2937A). The board is designed exactly as recommended with 0.1uF on the input and 22uF on the output. It didn't work... It's a 5V regulator and we were getting 4 point something unregulated out of it (with anything between 6 and 18V applied). The solution was a 10uF capacitor on the input.
We put an oscilloscope on the output, and it was "unstable" but not really oscillating. When we looked at the input it was oscillating. I chose to try a 10uF capacitor just based on "engineering intuition and experience". When it worked, I tried a 1uF capacitor and that worked on the 5 "prototype" boards we have. Since 1uF worked, I'm confident that 10uF is not a borderline value and it will make a good permanent solution.
The funny thing is, it's a rather complicated board with a microprocessor, RAM, ROM, Ethernet, RS-232/422, USB, 5V, 3V and 1.8V regulators, and the ONLY problem we had was a "foolproof" linear regulator chip. (I didn't design the board.)