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?
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My Bay window succulents.

My Bay window succulents.