To answer the OP, I will say no, they were not in a long term romance. Spock seem to have the least affection for Chapel of all the girls he uncounted who loved, liked or crushed on him. It was only Zarabeth that things were mutual.
In TOS, Spock showed more subtle attraction to Uhura than he ever did with Chapel though I do admit this was due to Nimoy and Nichols having chemistry and been dear friends, and Nichols been well Nichols. Most guys on tv had crushes on her, so TOS subtlly having guys like Kirk, Spock, President Lincoln and Sulu smitten by her was only a reaction from the audience even with the racism limitations.
A lot of things will happen in the coming seasons. I wonder if we will get like a time jump between seeason 2 and season 3 to speed up the 10 years, since we know Chapel becomes the Gunther of TOS and I mean Gunther from Friends who had a crush on Rachel as Chapel did with Spock.
By TOS, Chapel is not even among the core main 7 of the group. Kirk, Spock, Sulu,Uhura, Scotty, Chekov and Bones.
Now as a long time fan of the series, who is open to welcoming new romances. I will gladly have welcomed a spock/chapel romance wit no hold back as end game. if the writers had approached it more honestly and with less insecurities about another legacy character. So I am more eager to see the spock/chapel/tpring thing implode and Spock meets Leia and Chapel meets Korby where we can have hopefully more honest writing that respects TOS.