I've seen refiners run topped crudes through a coker, but that is very different than whole range crude. Given that your coker was designed for SR resid, i agree with comments above that your equipment can handle whole range crude processing in any considerable amount.
As also noted, i'd be concerned about coke morphology.
So my real question is, if this option is regarding operations post turnaround (i'm assuming this was a planned turnaround), why would this reduce "catch-up" time? Presumably you have a planning department that managed your refinery inventories properly?
In any regard, the whole point of refining is to maximize the margin by processing raw feedstocks. If you put crude through a coker, the refinery product yield will be absolutely horrible. Even though you are reducing feed inventory quicker, you likely won't be making any money doing so.
You should consider commercial options to get into better inventory balance. Even if you sell the crude at a loss, it probably is more economic than running it through a coker. Cokers make coke out of liquid product. Coke = 0 value.