We had one that didn't sing the song until the day she laid, and she sang for a few hours first. An EE sang for a few weeks before she finally laid. If you're concerned about where the eggs will end up, you can lock them in the coop during the morning for a few extra hours. You can always wait until they start laying to do that.
I have found eggs in a nests on the property on a few occasions. Mine are out from morning til night. The EE's are ALWAYS the culprit! They dont' wanna lay in the coop nests, they want to make their own nests and lay in them. I've found one nest near the woodpile, that has a piece of tin covering the wood. The tin overhangs a bit, and the hens think that's a fabulous place for a nest. They've reverted back to that same nest twice now. Another nest was in the garage on rocks! They made an indention in the gravel, and laid right there! So much for a nice, soft nest. The other nest was beside our burn pile, in tall grass. I had an EE that started laying in the basement window well. She laid there a few weeks, and finally went back to the coop.
If they are out, some will decide to lay wherever. Or at least that's been my experience.