Is an overhanging roof shelter enough to safely leave bike outside?

A roof is better than no roof, but not as good as an enclosed space because wind can blow through bring dust and dirt and moisture.

Sunlight is also a source of slow continuous damage. For years I kept bikes under a carport that was also sheltered from the sun, and while they still rusted, it was much slower than if they were out in the weather.

If safety means secure-from-theft then a roof makes practically no difference. If someone wants to steal it they will.

Airflow can be useful, but a closed dry space is good too. You want to avoid a damp airless space because that's not good.

keep it outside most of the year

If by keep it outside most of the year you mean that it will be stored outside but you will ride it and maintain it then outside storage is not as damaging.

If by keep it outside most of the year you mean stored, rarely ridden (once a month or less) and not maintained then you will see damage.

I've seen many bikes that were stored in a leaky shed or a roof only cover and never maintained. It takes very little time for the rain to wash the oil out of a chain and turn it into a solid mass of rust or rust brake and gear cables until they don't move. As Criggie says a roof is better than no roof but rain often does not fall straight down.

Here is a nice article on What Happens When You Leave Your Bike Outside

The bottom line: Leaving your bike outside for a day or two won’t do major damage. You may see signs of rust after a week of neglect. After one month in bad conditions, your beloved bike parts will start to degrade.

So I’ve built a shelter to keep the rain off my bike and intend to keep it outside most of the year. It’s just a sloping corrugated plastic roof to keep the rain off it.

Will this be enough do you think?

No.

I have stored a bike for around a year below a shelter outdoors. The bike was in such a location that no rain ever directly touched it but it sure was unprotected from humidity.

The result?

• Brake lever rubber hoods were so sticky after the storage that I had to change them. A simple roof doesn't shield from sunlight, and sunlight deterioration of rubber is rapid.
• Brake pad screws were rusted -- not so much that it would affect their function, but it sure looks ugly.
• Rear hub made of polished aluminum was severely pitted. Not so much that it would affect its function, but it sure looks ugly.

The frame of the bike in question is butted chromium molybdenum steel. Its outside surface didn't rust. I haven't looked inside the tubes, though. It's possible there's internal rust -- not so much that it would affect its function, but a perfectionist might consider even minor internal rust as a problem.

If you don't consider minor surface rust visible to the eye to be a problem, and if you are prepared to change all rubber parts you touch with your hands (i.e. brake lever hoods), then go ahead. But I think you will be far more satisfied in a better shelter, something that isn't humid and something that perfectly protects from sunlight.

I use a Dasbike cover for my bike that is stored outside.

It completely covers the bike.

I bought it mainly because of all the flying dust generated by the landscapers.