Is it feasible to do a Yu-Gi-Oh! booster draft?
Yes it is feasible. It is not so different from other Card Game Drafts, and it is briefly described here.

However, from experience, it is not fully feasible to do with any booster pack, and is especially difficult with the "main" Card Expansion Sets that follow the Anime, which usually are 100-card sets or less. In fact, I have never seen a Draft tournament made on such "main" expansion sets in the community I play. 

If you plan to do a Draft tournament I suggest you consider doing it with card expansions like Battle Pack 3: Monster League, its previous versions, or similar boosters. That link also describes on detail how to carry out such tournaments.

These Battle Pack sets are specifically made for draft or sealed pack tournaments, as they include a wide and balanced variety of cards. These are also bigger card set expansions (BP3 has 237 cards) which enable for a better gameplay. They also tend to be cheaper by the booster, something that makes it easily to afford and convince prospect duelists to join the tournament.