I dont think so. She never learnt the contents of the second letter. She was young and didn't understand why she came back at all. She still believes that her mother committed suicide because she couldn't become a singer or because it was too late to achieve anything.
True... she didn't read the second letter. But she could have as a child thought that somewhere her words may have been responsible. Because Nimki knew her mother didn't commit suicide after she came back but after hearing her words. There is a possibility that Nimki as a child could have made such a connection.
Anyways, this could be why Ram bacchan never showed the second letter. It would have been an extra burden on Nimki who was already unable to deal with the tragedy. It is one thing to think that her mother committed suicide because she failed to fulfil her dreams but all the more terrible to know that it was because her mother felt that she failed as a mother. And unfortunately, it seems like it was Nimki's words that really pushed her to take that final step... although one can't fault the child Nimki for what she said.