Yes it’s(UExampleObject) only going to exist in game and you won’t be able to edit its values in blueprint. Coming to your second question , if you enable the option (Run construction script on drag) it is going to run construction script of that actor and even if you disable that option ,every time you double click a blueprint to open and change any property or something , it is going to be reconstructed (C++ constructors are also called).
If you want to check it try putting some UE_LOG statements in constructors of your actor, component and also actor that you are going to create inside your Example component. Whenever you open blueprint to edit something in it you can see those logs printed ,immediately meaning that it is reconstructed (All C++ constructors and blueprint constructors are called). So,if you create your UExampleObject inside constructor of UExampleComponent it(UExampleObject) is going to be reconstructed every time you open blueprint. That is why I suggested you to create it inside BeginPlay() so that it is only constructed once during game play.
Coming to your last point ,constructor script and c++ constructor are not completely independent. There is an order in which c++ constructor and construction script execute i.e. all the c++ constructors are called first by the engine and then construction scripts. Later after constructors are called (also construction scripts) BeginPlay() of all C++ is executed first and then BeginPlay() in Blueprints. Although we cannot predict constructor and BeginPlay() of which class are called first, as far as I know that’s how execution flows . I recommed you to structure your code according to that execution flow.
And also I don’t know why yo are trying to create UObject inside Actor component ,if possible try creating every variable and method that you need inside your ExampleComponet that will save you the trouble of dealing that UExampleObject.
I hope this explanation clarifies your doubts,Cheers!