There are some contexts where I have it uploaded and I've uploaded it carry the same (relevant) information, so you could say they're "interchangeable" in those specific contexts. For example, suppose you're in a wi-fi cafe with a friend...
Do you want to listen to my new song? ...
1: I've uploaded it.
2: I have it uploaded.
(note that both alternatives above could reasonably be followed by something like ...into my public Dropbox folder, to which I emailed you a link this morning).
But in most contexts there would be at least a shade of difference in meaning (if the upload process was difficult/unusual, for example, the speaker might attempt to emphasise this by using the more "verby" construction #1). As OP suspects, uploaded in #2 is effectively an "adjectival" usage. Compare...
Do you want a beer? ...
3: I have some stored in the fridge. (past participle used adjectivally)
4: I have some cold in the fridge. (explicitly adjectival usage)
(where it's contextually unlikely the speaker means someone else stocks his fridge with cold beer!).
The construction TO HAVE [something] [X'ed - past participle] can also be used to mean to get someone else to X something for you (where context may imply either a "one-off" or habitual process; the syntax itself implies nothing on that front). But this is a declining usage - people increasingly say (He) gets his car serviced (by a local garage) rather than ...has his car serviced.