Can I store unused hardwood floor and base trim in a shed (or garage)?
I store flooring in my shed/garage all the time. However, the humidity isn't very high where I live.

You should find out the  max humidty recommended by manufacturer and verify that it won't exceed that.

Also make sure not to store directly in contact with concrete floors as they could absorb moisture through the concrete.

For engineered flooring I would not be very concerned about warping/distortion if you store it flat and even.

You should be more concerned with adhesive breaking down, wood finish failing, and fungus/rot. All of which would most likely be cause by too high moisture content.