I have a dilemma. I recently pulled off my gutters and fascia boards thinking I had leaks at my gutter seams. I discovered that the worst leaks were coming from the roof edges (20 year-old roof). I decided that I must have a new roof installed and contracted to do so. The work will begin in about a week. About half of my fascia boards have been removed (by me) and I have been repairing rotted wood and will do all of this work myself. I realized that it would be better to have the roof repaired prior to finishing the fascia work, since the rain water would just continue to leak in until the roof was repaired. So, I have just left it open and the rain water continues to leak in. My concern is that once the roof is installed and I finish the fascia repair (painting, etc.), there might still be moisture trapped inside that will cause the wood to begin to deteriorate again. If I complete the work too soon in an attempt to keep moisture out, I fear I may be trapping moisture inside. But if I leave it uncovered, to let it dry out completely, I risk more water getting in. It seems like a catch 22 situation. I hope I have explained this well and that someone could pass along some helpful advice in helping me solve my dilemma. Thank you so much.

Without the fascia on the drip edge will not be able to be installed correctly since it butts up to it.

He is right, do the facia first.
Check your soffit venting while you are at it.

You should do the facia first and any moisture that is still there will dry up and cause no harm to the wood. It will only rot if continually leaks.And if you do complete it have the roofer come and water tight your roof till he gets there. May charge you for it but you will sleep better at night.