Incidentally, a sentence such as "He ate the hamburger with relish" is ambiguous (at least in US English), and can mean:
Он с удовольствием съел гамбургер.
or
Он съел гамбургер с вареньем из солёных огурцев.
So, whether you translate Я вся в предвкушении as "I can practically taste it" or "I relish the prospect", there is a figurative connection with вкус.