Can clothes dry outside without sun?
Yes. Sunshine speeds drying but is not required. Dry air and a steady breeze will dry a full load on a completely overcast day, often faster than bright sun with no wind at all.
Wind does more work than sun
Sun helps in two ways: it warms the air, and it warms the fabric directly. Both give water molecules energy to escape. But escaping is only half the job, because the moisture then has to be carried away.
That is wind's job, and it is why an overcast, breezy day regularly beats a sunny, still one. Moving air strips off the humid layer sitting against the fabric and replaces it with drier air, over and over.
When cloud is actively better
Direct summer sun fades colours and weakens fibres, particularly on darks and on silk. Bright shade with good airflow dries almost as fast without the bleaching.
The exception is whites, which benefit from sunlight because it gently brightens them. Give whites the sunniest spot and turn colours inside out or hang them in shade.
The day to actually avoid
Not the cloudy one. The still one. Overcast with a decent breeze and humidity under 60% is a perfectly good drying day. Overcast with no wind and humidity at 85% is not, and no amount of waiting will fix it.
If you take one thing from this: check whether the air is moving before you check whether the sun is out.
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