Yes, I already had a Delta Gold and got the SPG. Got the 10,000 SPG point welcome bonus after my first statement. Note you have to get a NEW SPG card, not change your existing Delta to an SPG (if that's even possible).
I haven't hit the $15k spending threshold but am not worried about whether I will get the points if I do since I got the sign on bonus. From an Amex rep, you can only get one bonus on each PRODUCT per lifetime. This means if you got SEPARATE Delta Gold Amex, Delta Reserve Amex, SPG Amex you could collect all 3 sign up bonuses for new customers.
Also unofficially business and personal cards count as separate products so you could actually get each of the above x 2. No personal experience with that though.
And on another note, as you mention they do give bonuses as well for upgrading from dl gold to dl plat although they are not as good as for a new DL plat. I was offered 5k MQM with first purchase to upgrade from DL gold to plat (with normal extra 10k MQM per $25k spend threshold bonuses that are a normal feature of the DL Plat). However, I was not offered RDM bonus like I would get with a new DL Plat Amex.