Hi -
I had the same scenario occur very recently (we leave in a few days for the trip I was freaking about, below) and posted on Scubaboard about it last week. I suspect they will get to your paperwork, and in their support, all my friends with DEPP have had no issues with reimbursement. However, from my standpoint, it is nerve-racking waiting for them...and perhaps - um - someone needs to suggest to them that they not swear up-n-down in their voice mail message that they will call you back within 24 hours. 
Why it irks me that I have DEPP insurance....
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I have DAN equipment insurance right now, but I have been wanting to switch to DEPP ever since I made the switch to dSLR - I really like the whole "drop overboard and it's covered" aspect, and I am also a fan of the fact that you can CHOOSE what is insured against flooding. I like having my drysuit insured against theft/loss, for instance, but not so sure that I am interested in flood insurance for it!
So maybe 2 months ago, I called them. I spoke with a woman who let me know what needed to be done to set my policy up. I did what was asked, faxed everything in, and nothing. Days go by. Weeks - more than 2 - go by. An upcoming trip was approaching, and I was starting to panic. I called them and left messages, about 4 over a period of a week. I heard back NOTHING. I did not receive any phone calls back (as requested), emails (I do check my junk email), faxes...nada.
I finally - after a month of waiting - called DAN and updated my insurance with them, even though I really wanted to switch to DEPP.
Yesterday, I got home from work, and awaiting me in my snail mailbox? You guessed it. My insurance policy from DEPP. I immediately called them, explained the situation, and asked to have the flood premium refunded - everything else, I decide to keep for now - at least a few things will be covered if they get dropped. The woman I spoke to (who shall remain nameless) insisted that they had emailed me the policy twice - they certainly had not, as I had anxiously been waiting for it and checked my junk mail folder daily.
Then the kicker. She tried to tell me that my DAN policy wouldn't cover any floods that occur outside of the US - I believe the exact statement is, your stuff will not be covered for international travel. Unless the DAN insurance website is completely incorrect, THAT is an out-and-out lie. From their website:
Territorial Limits – We will cover property wherever located (worldwide).
Sadly, I still want DEPP insurance....at least now I have a small policy so that I can alter it to add everything I want in the future....