Deploying existing Elastic Beanstalk inside VPC without deleting the RDS associated

I've currently in production a beanstalk with loadbalanced instances, and an associated RDS. Also got some routing/dns configuration that allow me to call my beanstalk with a "straight" domain name.

I'm in the need to assign a static IP my Elastic Beanstalk Application so I can give it to a 3rd party that will need to whitelist me so I can call it.

I saw, regarding this link, that this can be achieved with VPC

I followed the procedure except for the RDS part.

Now I think that I need to delete my environnement (so the DB too) and launch it again within the VPC ? But is there a way to do that without deleting my -prod- database ?

Also, will this procedure change any behavior for my existing setup ? And will it work fine ? I mean as far as I can imagine, here is a theorical situation:

-Some user enters my portal from this url http://awsomeDomain.com (which ends to my beanstalk instances). He try to 'identify himself' so I make him enter his cellphone number. Now I got it and I want to call my third party with this number to it tells me what is the state of this phone number.

Will I be able to, inside my php code (from my beanstalk) make this call From the elastic IP assigned to my VPC ? It is a bit confusing to me as far as I feel like using this VPC is more of a trick than a real solution and that I don't use it on it's main purpose.

So right here I got my VPC, basically configured (from the tutorial) and I'm not sure what to do. Thanks in advance