Yes, the bags will do the job, but you have to be sure to get them under the culverts too. Then when they are all in place and rebar is driven through them, you have to pour loose sacks in between the culverts to fill that cavity. Like everything, it's all about the small details.
If it was me, I think I'd reset the culvert, then build a form with plywood and lumber to pour a solid wall. The angle of the culvert won't matter if the entrance and exit of the culverts is protected by cement. Left unprotected, the water will just keep wearing away at the edges of the culverts until they fail. It's a time thing, and water always wins with enough time.
Another option would be to pour a brick ledge on the concrete wall and tell the client that you could come back at a later time when they have the money and put in rock vineer. With the brick ledge in place, you could do this at any time and until then, it would still look good. You might get two jobs out of one!!!
Eddie