Does the body prioritise the use of available sugar before fat?
In a very simplified explanation  - the body usually picks the process which is easiest/ fastest which would be to absorb the glucose  then the fat would be used for energy as this takes longer to digest and absorb because it is a relatively complex molecule which also requires bile to emulsify it.

Starchy/ high glucose products will already be broken down in the mouth by amylase and absorbed in the intestine + pancreatic amylase etc. which takes around 20 mins-1hr whereas soluble fats are digested primarily in the small intestine (by enzyme lipase) for (very approx.) 1-4 hours depending on the amount ingested. Insoluble fats are broken down into soluble fatty acids and glycerol which can be absorbed into the blood. 

The amount of either you use for energy just depends on how much energy you expend.