Again, if they think Weber has legit upside as a Running Back, then his Special Teams ability (as a rookie) won't really be the decision criteria.
It's highly likely that the game day RBs are Zeke, Pollard and Olawale regardless of whether another RB makes the 53 man roster.
I know the media and commentators will constantly ramble on about players needing to play special teams to make the roster; however, teams keep some players for developmental purposes and don't plan to make those players active on game day unless another player at the position will miss a complete game.
In the specific case of Weber, Olawale has ST ability and Pollard projects to play special teams; therefore, if Zeke missed a game and Weber was active, they still have 2 ST RBs in Pollard and Olawale in either situation.
If Weber makes the team as a developmental player, then they'll expect him to learn Special Teams over time, but his ability on Special Teams as a rookie on cut day is unlikely to be a big factor due to him being the 4th RB.
Weber will be the 4th RB even if he looks better as rushing than Pollard because they'll going to use Pollard as a multi-dimension player (runner, receiver, blocker) because that's what he did in college.