Yes, the new cory seems happy to me and the behaviour of the new one is absolutely normal. I am really pleased to see the new cory acting so normal and happy. They do chase each other all the time, but I haven't seen that happening to any other fish. So it's the way they interact with each other.
Aquascaper reckons the old cory will stress the new fish to death again I guess

. If you want me to show you aggressive behaviour when introducing new fish, watch one of my fish on the video below. It was just after I added corys to my tank, my swordtail took a dislike to them. This lasted for weeks, not for a few seconds which is the case here.
http

/www.youtube.com/watch?v=TRR5hZErhfc
And a video below of my corys chasing each other. Wondering why they never chased the guppies or the platies

They used to abuse the pleco a bit getting on top of him when he eats. These corys are a colour morph of the same species so they do interact with each other and even tried to breed together. But julii and peppered corys are completely different species and a few of each kind is desirable. They will get on together, but they get on with any other type of fish as long as it's not big enough to eat them, but if you want them to be happy, it's best to up the numbers of each type.
http

/www.youtube.com/watch?v=OzsGiJhRBnk