It is my personal opinion that the more the Android learns human knowledge, the more human he becomes. The very yearning to be so is human in its own right. If I understand, the emotion chip causes malfunctions but I think observation naturally could give him some kind of emotional function. I haven't yet seen where he's got said chip but it seems like the more he learns, the more human he is. I still have yet to see In Theory as well but apparently, he gained a relationship with a hologram in some way and on Data's Day, he clearly believes he would be married someday AND even said he understands love and friendship. I can't see how it'd impossible to gain a relationship with someone even without emotions - he does have a conscience and morale. I am needing more interesting research for a fanfiction I'm writing.
I'm going to say no. Firstly, it's explicitly stated in several of the scripts that emotionality will always be beyond Data, even in situations where he can clearly identify that an emotional response would be appropriate, for example in TNG: The Offspring where his daughter dies:
DATA : What do you feel, Lal?
LAL : I... love... you... Father.
And Data just stares at her... unable to say it back.
DATA : I wish I could feel it with you.
LAL : I... will... feel... it... for... both... of... us.
PICARD : The crew grieves for your loss, Mister Data.
Data studies the sad faces of his "family", never has, never will entirely understand "grieving".
and in Star Trek Generations, Data himself gives us a pretty good indication that without the chip, he's reached the end of the road as far as his growth (as a person) is concerned.
"I thought you were afraid it would overload your neural net." "That is true," Data replied. "However, I believe my growth as an artificial life-form has reached an impasse. For thirty-four years I have endeavored to become more 'human'- to grow beyond my original programming. And yet I am still unable to grasp such a basic concept as humor."
He turned back toward the crystalline case. "This emotion chip may be the only answer." Geordi leaned forward to dubiously study the chip, then sighed. At worst, it could cause some annoying complications, but no permanent damage. And what right did he have to deny his friend such an experience?
I think Data would be able to develop responses that were perhaps rudimentary feelings. It started by imitation, but there were times where you can tell from his reactions that the "imitation" had some sincerity.
My best evidence: "The Most Toys". It's probably the most emotional you ever saw him before the chip, and so much more satisfying as character development. He became angry and was going to kill Fajo. I argue this because he recognized it as an emotional response. Had it been a logical decision to protect future victims, Data would have reported it honestly.
Yes it is possible. First, from everything we have seen in Trek, anything is possible. Probability is the problem. Second, what is emotion other than learned behavior brought on by observed contextual clues of your surroundings, i.e. social and evolutionary programming. Data is capable of learning on a mental level, not just rote memorization.
That said, Data and his creator both know there are natural technical limitations to Data, that cannot be overcome by sheer willpower. Hence the chip. Note that Lore did not have those limitations in place, him being the reason for Data's limitations, and nor did Data's mother. And possibly neither did his Daughter.
I think the best evidence we have of this comes from
my Soong in TNG 'Brothers':
Basic emotions. Simple feelings, Data. Your feelings. I've imagined how hard it's been for you, living amongst beings so moved by emotion.
The fact that Soong knows Data doesn't have emotions suggests he knows Data couldn't develop emotions without some alteration. So, I'd say that Data couldn't possibly develop emotions without some external input.
Yes, as we saw briefly in the episode Deja Q. At the very end, Q gives Data a brief gift of laughter. How did he do this? All powerful trickster god, who knows? But it would seem to hint that the possibility is there. However, as a practical measure, convincing an all-powerful trickster god to give you emotions is...probably not a practical solution. So in terms of personal evolution, no. In terms of perhaps altering some of his code or whatever, probably. No reason the code of a chip can't be integrated into the system. But the danger there, of course, is that nobody but Soong is competent to do such a thing- and look how well that turned out with Lor.