The conventional thinking in terms of the #10 pick is that we need either a point guard of the future or a swing man to provide scoring off the bench. While I admit these are more immediate needs than adding to the current glut of frontcourt players on the roster, I would argue the Hornets need to be thinking about long-term team construction, not fitting in pieces around the existing mediocrity. The team as currently constructed will be competitive in terms of fighting for a playoff spot but much of the current roster is unlikely to be present when the core comprised of this draft and probably Eric Gordon competes for a title. This is why instead of focusing on immediate need, the Hornets need to be thinking in terms of long-term fit with Anthony Davis and the best available player, and Sullinger if available at #10 would be be both.
Sullinger has a lot of desirable qualities and a few obvious ceiling-limiting deficiencies. He has easily the most developed post game in this draft, a quality jump shot with range approaching the NBA 3, is a strong offensive and defensive rebounder with a great understanding of positioning and better-than-advertised length, an excellent basketball IQ and good passing out of the post, and a large body ready to bang in the post from day one with the toughness to do so. His deficiencies are that he is an average athlete with poor foot speed and defensive quickness, is short for a 5 and slow for a 4, lacks the ability to alter shots and act as a rim protector at the pro level, and may struggle to adjust against longer defenders at the NBA level.
The reason I believe Sullinger is a uniquely good fit for the Hornets is that nearly all of his deficiencies, particularly his defensive liabilities, would be disguised by playing next to the best shot altering prospect in recent memory. In turn, he would provide the size and strength to match up with more powerful centers and power forwards without getting backed down and conceding post position and would therefore allow AD to roam, wreak havoc on help defense and in passing lanes, without having to body up with players who outweigh him by 40+ pounds. Offensively, he would provide the post scoring and back-to-the-basket game which Davis can't yet provide, whereas Davis is an elite above the rim finisher and can make plays with his speed, length, and hustle in a way that Sullinger can't because of his weight and lack of quickness. Both players will immediately be plus NBA rebounders, and down the road with Davis' development could have two big men with consistent 20 foot range, passing ability, and post ability. They are also complementary in terms of personality: Davis plays with quiet intensity whereas Sullinger is vocal, emotional, and fiery in a way reminiscent of David West.
The obvious concerns are that we already would have 4 NBA quality big men on the roster who should play minutes, and that neither of these players is currently a 'true' 5. The first is a real concern. Young players develop best with a consistent role and minutes, and it's hard to find consistent minutes for 5 bigs. The Hornets may need to look into amnestying Okafor, or moving one of the backups---but in terms of our long-term plans, these players only enter the equation as backups. In a worst-case scenario, they could end up hurting each others' development like the Baby Bulls of the early 2000s, although I believe we're a better organization with better coaching and structure than those teams and also believe both of these players are more skilled and prepared for the rigors of the NBA than Chandler and Curry were. The second concern is almost universal in NBA frontcourts. There simply aren't very many 7 footers who are good, skilled, and tough enough to be the platonic ideal of a center. Unless you pay the price, buy a lottery ticket on a guy with limited basketball accumen and hope, pray and wait for the rare player who actually develops, you aren't going to get one. But Davis and Sullinger are both already terrific basketball players and together can do everything you'd functionally want a frontcourt to do plus some other great, unique abilities. It's unlikely that Sullinger even falls to #10; with similar players like Kevin Love and Greg Monroe enjoying success, and even players like Dejuan Blair outperforming many high-ceiling lottery picks, someone is likely to pick him up. But if he does fall, the Hornets should think hard about pairing him with Davis.