He definately has something, not necessarily human emotions, more like an android variety (like when he snaps at that guy in the Klingon civil war ep)
I wouldn't use that one as an example. That was a processed reaction. He knew that he had to act that way in a command situation, especially with someone who did not know him or understand him. This was the only response that would fit the situation, & Data knew that & approximated the appropriate response. He has been in command situations before
Having said that, I think this question is one of the hallmark subtle gags of TNG. Does he have emotions? Not Human emotions, not until the chip. Vulcans don't even have human emotions. That's why they have to suppress them. They're stronger than Human emotions, which explains why Romulans are so much more emotionally over the top than Humans
It stands to reason that if, in this universe, there are beings with emotions stronger than human ones, then there might also be beings with more subtle emotions. I think Data falls into that Category
The best example I can think of besides apparent ongoing morn for Tasha, comes from "Data's Day"
"It is fortunate that I am able to perform my duties without emotional distractions. If that were not the case, a sudden course correction toward the Neutral Zone would make me very...nervous. " He says, while, at that very moment, nervously tapping his fingers on the console, & then recognizes that he is doing so, & is even surprised by it himself, noting his own subconscious manifestations of anxiety.
If that isn't suggesstive of something purposely written into the story to point us in that direction, than I don't know what is. It may not exactly be fear in the pit of his stomach, like a Human might feel, but it's.... something, & the writers wanted to toy with us about that