There are actually two parts to consider... passing the ECID (and making sure that the App's ECID overwrites the ECID cookie on the website) ensures that Adobe sees this person as the same user. Once the ECID cookie is set, then yet, the rest of the journey should use that ECID to identify them.
However, since you are talking about a promotional banner, I would recommend setting up "Internal Campaign Tracking", this is usually an eVar set to Visit level attribution, and pulled from an internal campaign query parameter....
If you site uses "CID" for campaigns, you would probably want to set up an "ICID" (internal campaign), if your site uses UTMs, then you will want to set up at least one ITM (now you won't need a full spectrum of values like UTMs, since you already have a lot of information about this user anyway), I would start with something like ?itm_campaign=xxx, then set this internal campaign to something like "app_promo_x" or whatever you need to identify this particular banner. You can use internal campaigns within your website too, for web promotions.
Then when you look at your conversions, you can look at your externals (Marketing Channels or Tracking Code, etc), and then you can look at your internal campaigns separately.... Keeping your Internal and External Campaigns separate allows you to understand how people are being driven to your site vs what elements within your site are contributing to your conversions... and you can always correlate your externals and internals together to get the interaction of the two drivers.
