No. The Borderlands 2 DLC Captain Scarlett does not raise the level cap and keeps it at 50.
The following is taken from a GameFaq Forum:
Down in the Gearbox Forums, one of Gearbox's PR guys came into a topic
and said that for that trailer they had 52 points simply to access all
the skills for the video.
So no level cap increase.
Scroll down to Adam
And in the GearBox Forums themselves:
Re: Video: Sir Hammerlock Introduces Gaige the Mechromancer -
Yesterday, 02:29 PM
dovidf5024: Lvl cap raise then?
Adamf: No. Just using our tools to record footage and change our character on the fly.
This response came from the fact that, in a video, Adam had a character with 52 skill points, meaning that the level required to attain that level was 56. However, he pointed out that he just edited the character to show the different aspects of the new character.
I can only say that there MIGHT be a level cap increase. But Captain Scarlett definitely does not introduce a new level cap.