Seedling question

Seedling question

I've got a number of successful cucumber seedlings (first true leaf showing) that I have to transplant into something with more root space than the cardboard egg carton cups. My question: they're all quite leggy -- about 3" from soil to leaf. If I bury most of the stem when I transplant, will it grow more roots and give me a stronger plant (like a tomato), or will it just rot and die?
Purple Coneflower?

Purple Coneflower?

morning glories…..

morning glories…..

My New Apt!

My New Apt!

okra

okra

Please identify this bush!

Please identify this bush!

plant ID plz~

plant ID plz~