At a general level, I state that an applicable law has to be complied with. Referring to your specific query, I will answer in the negative first and then ask you to read both the acts for improving your own proficiency. Do inform us what you will find!
Compliance with the Information Technology Act
At another level, I inform you that under the provisions of the "Information Technology Act" (I think it was passed in the year 2000), it is clearly provided that if any record/information required to be maintained under any act is kept in electronic format, then that will amount to compliance under the basic act that required you to keep some record. The fact that not too many organizations have resorted to this method is true, and I dare say not many HR professionals have particularly looked at it.
I suggest you obtain a copy of the IT Act and study it. You don't have to be a lawyer to understand it!
Regards,
Samvedan