I doubt it. As the years go by, more efficient data storage options will become available to us.
A few decades ago, a kilobyte class memory device was so large it had to be placed in rooms and so heavy it required multiple people to move it around.
Now, a 32 GB SD card is so small that a friend of mine once put one in his mouth and mistakenly chewed it.
The Advent of DNA based data storage will drastically change how we store information. The data on the blockchain isn't crashing anytime soon.