Let me open up saying that anything is possible. Anything. The context is generic, largely because guidelines on how to interpret the history of the Cincinnati Bengals is guided mostly on the radical changes that Cincinnati has made in recent years.
It boils down to value. If there's a player that they like, well-placed on their draft board with an accompanying value, then obviously the Bengals will pull the trigger. They did with tight end Tyler Eifert -- relatively unexpected based on the needs that were identified that year. We're projecting more Best Player Available themes this year, similar to last year.
On the other hand, if they don't see the value at No. 24, they may even fall out of the first-round (or at the very least, later in the first).
They did that in 2012. Instead of using their No. 21 pick to select a projected offensive guard, the Bengals completed a trade with the New England Patriots to No. 27 to select Kevin Zeitler -- Cincinnati had graded Zeitler and David DeCastro, the other top guard in that year's NFL draft, evenly. A benefit for dropping six spots? A third-round pick (which became Brandon Thompson).
We can say with some certainty that the Bengals won't move up in the NFL draft. The argument that hopes for it, applies the fact that Cincinnati's roster will remain largely identical to the '13 squad -- so the need to draft players isn't that big of a deal for depth. Those experiments have failed in the past and Cincinnati doesn't have a dire need to upgrade a position -- quarterbacks be damned!