No, she was stone-cold sober and it was completely planned. Refer to the book The Late Show by Bill Carter (an account of the Leno vs. Letterman battle over who got the Tonight show) for other instances of Connie’s sometimes tone-deaf sense of humor.
She doesn’t look hammered to me. She looks like a normally serious person who got talked into doing a humorous sketch and it is failing. Look at 50% of the guests on SNL for more examples.