You can if it acts as an open channel. The complication comes in when either the upstream or downstream end of the culvert is submerged.

mannings can be used for calculating normal depth with uniform flow in open channels. culverts rarely flow with a uniform depth, so it really only applies to longer conduits or open channels.

you also need to factor in the tailwater and entrance losses. for a "short" culvert, these are highly critical and may totally override the normal depth. so most culvert capacities are a function of the inlet or outlet conditions.

To expand on cvg's point, storm drains are typically hydraulically long; in that they can reach normal depth unless influenced by other controls like tail water. Storm drains also experience inlet & outlet losses which is alluded to by the term "other controls", above.

Culverts are typically short as cvg points out and experience more rapidly changing flow regimes.

Hopes this helps.