If you apply and are approved for the Delta Gold, the SkyMiles from the bonus are transferred into your Delta SkyMiles account, so there's no danger of Amex doing a 'claw-back' later on if you decide to close the card.
That being said, you can only get the bonus once per lifetime per Amex product, so make sure you "make it count". There are various bonuses amounts for the Delta Gold, and unless you have one of the more generous ones I would likely wait, unless you're an avid Delta traveler and would benefit from the card otherwise.
Also note that in the past people would convert the Delta Gold over to the no-AF Hilton HHonors Amex after the first year to avoid the annual fee but still keep the account open, however this is no longer an option. With Amex you now are only allowed to PC cards within the same family or Amex Partner.
Here's a link to a thread if you're interested in the recent changes to Amex PC criteria:
Hope this helps! 
@Anonymous wrote:The bonus would be 60k which from what I have seen is a pretty generous award offer. That said, i really would only want it to get the sign up and then close the card. I did just apply and get approved for AMEX ED card so I am not sure if after 10 days or so I would get another HP if I did go for Delta Gold
You're right... the 60k bonus is the best I've seen as well.
You can expect another HP when you apply for the Delta; the only time you can (usually) get a 2-for-1 is with a charge card and a revolver in the same day. Any other combination (or on different days) generally results in two HPs (this is just what most people report, as always YMMV).
There's nothing keeping you from closing the card right away, but since it doesn't have a fee until the second year, if it were me I would hang on to it at least for a little while if for no other reason than to get the checked bag for free benefit. Once the account is opened it will impact your AAoA, so there's nothing to gain by closing it right away.
That's completely up to you, of course. I'm just sharing what I would do in a similar situation.
Let us know if you get approved!
@Anonymous wrote:Also just realized, I got it in the mail, i see it online now too but if I go to AMEX.com to check pre qualified offers, the delta card doesnt show up. Don't wanna get declined and waste a HP
I didn't prequal for anything and I still got approved for the BCP and a Green card.