Is a threshold drain outside my laundry room and bathroom, draining to daylight, a good idea?
I see several problems with your plan:


It may allow mice, insects or other critters to get inside.
If it's below freezing outside, the drain will get blocked with ice.
The check valve (even if it works properly in the first place) will very quickly get clogged with all the debris that gets washed down into the drain.


If you want to have a floor drain, then it should drain to the sewer, not to the outside. I don't know what the building code in your area says about that, but you may want to check. And you don't really need a floor drain. It's nice to have in some settings, like a commercial kitchen or a public bathroom, but it's overkill for residential.