That is a really good question about plastic and seedlings, though it's a pretty short exposure time for most plants, depending on species and region. What would be your other options?
Depending on the region, this could be great, but with drawbacks. In our area, light for seedlings is at a premium, so the mini-greenhouse would be great if you didn't have a full-size one. I would be watchful, though, for damping-off, which can be a problem in soggy regions (make sure all drainage is perfect). We would have to bring the pots back inside at night anyhow, because night temps are too low here.
Plus, the milk jugs would need to be clear, which is harder to find these days.
I have had great success in planting seeds straight in the ground and topping directly with a cut-off jug.
Anyway, it sounds like it's worth a try! Depending on what you start, when you start it and where you live and where you store the jugs at night (etc. etc. etc.) you could have great success.
I would not overthink the plastic (though, wow, yeah, I never thought about it).
Good luck! And do report back!
"She is a mermaid, but approach her with caution. Her mind swims at a depth most would drown in."