I guess so. But I guess I get "Them Feels" about any character I bond to in any show. For example, Lets say the show is centered around...Braeburn even! And Poor old Braeburn was upset for some odd reason. I would get a touch upset I reckon. Not literally, "Oh gee, I am rather upset!" but I call it..."Them Feels" And it works the other way too! Imagine if Fluttershy is hugging Angel Bunny, and they are both ecstatic to see each other. At that moment one of my roomates might ask my why I am grinning from ear to ear and looking so happy. "Them Feels" So I guess I go beyond the mane six...Hope I helped hunter?

The Feels are strong with this show. The ponies that affect me the most emotionally are pinkie pie and fluttershy but mainly pinkie because she reminds me of me.

For me would be fluttershy and twilight....um I may be more of fluttershy, but I do carry some twilight within me. So when  their emotions happens, I feel its badly.....

I honestly think that the show is more aimed at teaching people how to deal with these problems in a subtle way. After all that is what television really does, It is a set of images that made to provoke interest, emotion and thought. 

We all relate to characters Differently after all 

I mean i love Rarity because she easily the most diverse and realistic character in the mane 6.. She has pretty much done everything else that the other 5 have been through but they haven't been as focused...

She has had her work stolen and copied when entering a very important competition for her, and she ended up coming out of it stronger
She has had to deal with the fact that her sister dislikes her, and wanted to compete with her even if she was not keen on the idea. 
She has learnt that fame and beauty comes at a price when her wings evaporated, and realised her mistake and apologised...
When she was kidnapped, she did not give up and simply used her strengths to make a dark situation into something positive.

There is a lot of positive  things that can be said about each character and if i had the time i would list them... people have different opinions on personalities after all if i met someone like fluttershy or rainbow dash in real life chances are i wouldn't get on with them...