Probably no. Twitter is good as it is: a mean of comunication
The Facebook Status and the Twitter status are fundamentally the same thing. You are telling the world what is on your mind. The like functionality in Facebook is a means of communication - someone clicks like and says I like your opinion on this, your good news, your joke, the fact you are in a good mood. Now if Twitter has the same status functionality could 'like' not be equally effective?
However they are used in different ways, by different users for different things. People mostly use twitter as a 'microblog'. It's like a blog, but each 'blog post' is limited to be very small. People use Facebook status updates to tell people what they are doing and to tell their friends things. If I see your facebook updates, you can see mine. Twitter is not like that. Facebook is for socializing, twitter is like newspapers. They are different, ergo it doesn't make sense to make them identical