I see no reason for any delay. However, you will have to do biometrics twice because of the two applications. Hopefully you will get the biometrics notices for both before the appointment date for either of them, so when you go to the appointment for the first you can bring both notices and ask if you can get both done right there instead of having to return at later date for the second one.
Although they will send the reentry permit overseas to a consulate of your choosing, they will not send the GC overseas. So you'll need somebody in the US to check your mailbox for the GC. Also note that you don't need the GC to enter the US if you have a valid reentry permit.