Oil finish on dyed wood

Shouldn't be any reason why you can't; shouldn't matter whether you use alcohol/water based dyes or stains; keep in mind that tung oil or Tru-oil AREN'T 100% clear, but have a slight yellowish or amberish tint to them. This may very to some degree on the type/brand of tung or Tru oil and could impact the way the color dye looks. For example, no problem with browns/tans/ambers/yellows, but a blue dye job might shift slightly greenish with an oil top finish.