It depends on what you are growing. There are many many threads here about this problem and in Growing under lights. Do a search.

Agree that it all depends on what the plant is and how bad they are. Most, but not all, can be fixed by deep transplanting. But as taz said, there are 100's of discussions on how to prevent them and how to fix them. Just search 'leggy seedlings'.

But no, without some sort of fix, depending on how bad they are, they won't be ok. The stem is the plant's circulatory system - it's food and water supply - and it is weakened and damaged when stretched and skinny.

For future reference, the humidity dome should be removed as soon as the first few seeds in the tray germinate (break the soil) and placed immediately under the lights with the lights as close as possible.

Dave

Here is a good start on reading about leggy seedlings for you.

Dave

Here is a link that might be useful: Leggy seedlings discussions

I see on your other post on the Tomato forum that we are talking about tomatoes. They are quite leggy per your pic posted there. Tomatoes benefit from deep transplanting ASAP. Bury them right up to just below the leaves and then provide more, closer light or they will just get leggy again.

Dave