Is it okay to be emotionally connected your RP character?

I saw this meme from the Tumblr blog Fuck Yeah Roleplay Rabbit (which is often brilliant but sometimes cryptic), and it got me thinking if it’s okay if you get a bit too emotionally invested in your character? 

We’re only writing characters, who exist nowhere but in our own imaginations. But they feel real, especially when we’re sharing them with other players in our roleplay. But is it a bad sign when you’re actually sharing emotions, getting sad when they’re sad, etc?

The author of FYRR writes this:

All I’m going to say is I am FAR too emotionally invested in this thing and whenever my characters feel down or upset, I will literally sit and sob at my screen. Especially when two characters don’t get along that, by rights, should do.

Is it good or bad to be emotionally connected to your character?