Is it possible to submit every March Madness bracket?
The rate-limiting factor is the cost of submitting each of those $2^{63}$ combinations.  Since submitting a combination probably requires (at minimum) opening a network connection and sending the combination to a remote server, you can generate combinations a lot faster than you can submit them.  Similarly, the cost of storing the submissions is probably negligible compared to the time it takes to submit them all.

In particular, if it takes one second to submit a proposed combination, it will take you $2^{63}$ seconds to submit all $2^{63}$ of them.  That's about 21 times the age of the universe.  If it takes you one millisecond to submit a single combination, it will take you $2^{63}/1000$ seconds to submit them all -- that's about 300 million years.  Obviously, not possible within your lifetime.

Also, note that the contest rules specified a maximum of one entry per person, as well as a maximum of 15 million submissions (not 15 million per person; 15 million total -- once there have been 15 million combinations submitted, the contest closes). Consequently, your proposed strategy simply wasn't possible.  The creators weren't dumb: presumably, they thought of that and made sure it wouldn't happen.