I can, and have done this, as a Si dom. Sometimes my recollection is instant, sometimes it takes hours/days/weeks to conjure up, and sometimes I don't ever make the connection.
I too, prior to externally laying claim that what I am perceiving is the end all, be all, sometimes have to do more 'work' to be sure of it. So that part I don't think is exclusive to Ni.
Like other's have said, I believe that if you know a person or have some understanding of the underlyings, or the Ni-er takes the time to explain it, that a non-Ni also can make the connection.
I know this guy- a public speaker. When he speaks, people say he goes all over the place with his points, but when he brings it home, it all makes sense. He wraps it up neatly (well, sometimes). That's Ni. I love how he takes seemingly unrelated things and is able to make connections, or use them to support his conclusions. Sometimes as he's setting up his points, I'm able to make the connection before he actually says it. Not that I am using Ni, but at least my Si ability helps me to follow what he's saying and build right along with him, not look at him with the
face.
Si and Ni are explained in polar opposites- with Si being so simple and straightforward, and Ni being so complex. Neither is the case.