Ask Mr. Smarty Plants

The only reference material we could find on this subject is from Arizona Master Gardeners Preserving an Agave Stalk. This apparently involved using it outside as a nest place for bees. Not sure that's what you had in mind.

Similar questions previously asked of Mr. Smarty Plants:

Cutting an Agave stalk in Corpus Christi TX

Century plant stalk from San Antonio TX

Preserving agave stalk from Sedona AZ

From the University of Florida Extension Drying and Preserving Plant Materials

If you follow the natural process of the blooms, they are for the purpose of setting seeds, for the continuation of the species. Some time ago, some volunteers (including this one) were working on agave seeds for the purpose of cleaning them and preserving them for the future  in a Seed Bank. They were not attractive at that point. It's really quite straightforward, the agave blooms, the blooms produce seed pods, the seed pods are rather ugly and black, and then they fall off.

If you have the time and the stalk, you could certainly do some experimentation on your own. You could try taking down the stalk before the blooms changed to seed pods. Our intuition tells us this would just mean the blooms would die all that much more quickly, and all the years of productivity that the agave had spent producing those  blooms, which is fatal for the agave, would be wasted. And the dead stalk would be constantly dropping stuff on the carpet, so we would certainly recommend that you keep it outside.