Ayn Rand's philosophy is that of a free economy that stresses the importance of the individual. A democracy is a political institution that stresses the rule of the majority. Rand idealized the self-sustaining individual. A democracy by definition cannot be sustained by one individual. So, it's a difficult analogy to make.

A better analogy would be like saying that a king has a right to abolish his monarchy.

Also, it is only self-defeating if the original goal was only to amass the wealth.

To continue the analogy to this point, a king abolishing his monarchy would only be self-defeating if his only goal was to be a king. However, if his goal as king was to make life better for his country, then abolishing his monarchy in favor of a democracy would be a very good move and not self-defeating at all.

Likewise, if the person's original goal was to produce and then dispose of the rewards as he wished, then doing so is not self-defeating. It's only self-defeating if his original goal was to simply have wealth.

<edit> The other part of Rand's argument is that the individual has the right to dispose of their wealth however they please, because they produced it and they own it. A democracy would only have a right to dispose of itself provided it was the democracy that created itself in the first place. </edit>