If you want to play it safe, you should submit your paperwork AFTER you move.
Steps:
1. Send application to Service Center with jurisdiction over your place of residence.
2. Service Center processes application, send you a Fingerprint Appointment
3. You get your fingerprints taken
4. Your interview is scheduled, appointment notice mailed to you
5. Your file is forwarded to your local office for interview
6. Interview/Exam
7. Await decision
8. Swearing in
As said above, depending on your local office, this process ranges from 6months-2 years.
Should you submit a change of address before Step 2, you should be ok.
If you submit a change of address between Step 2 and 3, you should be ok as long as you receive your Fingerprint Appointment and get your fingerprints taken. Otherwise, it will be delayed and won't move forward until you do step 3.
If you submit a change of address at ANY point after Step 4, you will very likely delay your case by at least a few months.
How?
For example, lets say you didn't receive the Interview Appointment and miss it. It can take time to reschedule, or worse case scenario, your application gets closed for failure to appear.
Or, if you submit your change after Step 5, and the local office receives it, they'll forward your file to your new local office in Philadelphia. You then wait for them to reschedule, etc.
Just hold on to your paperwork and mail it after you move, imo. It could save you time/money in the long run.