Thanks for reaching out to Ask Lafeber.It’s unfortunate that they built their nest there. I’m guessing this is probably a new or inexperienced pair of birds. To answer your question, yes, every time you open the door, they will fly off the nest. Eggs need a constant incubation temperature in order to hatch. This also goes for newly hatched babies; they need to be kept warm until their feathers come completely in.
Finch eggs normally hatch between 12 and 16 days. The variable in the days depends on when the parents start to incubate the eggs. Sometimes birds do not start to incubate the eggs until the second or third one is laid. This gives the first chicks that hatch an equal chance to thrive because they are all pretty much the same size. It’s not uncommon for the later chicks that hatch not to make it because they are much smaller and they are at a disadvantage when it comes to being fed enough to thrive. Often the larger chicks get fed first or the smaller ones get stepped on or not fed at all or not enough.
I suggest once you’re sure the eggs will not hatch, to remove the nest and wreath from your door. The chances of the parents wanting to nest in it again are quite high. You might want to think about substituting it for something less desirable or impossible to build a nest in.
Good Luck,
Debbie