In short, no. With no knowledge of sedimentary processes, chemistry of ores, or continental-shelf subduction, the ancients were completely dependent on surface geology for location of ore bodies. However, this was not usually a limiting factor - given that the world population only hit 200 million during the Roman Republic, and 500 million in the 15th century, the readily available surface ore deposits for most elements was usually sufficient. Regional differences actually stimulated trade and exploration, such as for British tin or Cypric copper (the origin of the name).
This is not to say that underground mining didn't exist - it certainly did from at least Roman times. But the mines were dug into cliffs and escarpments to follow seams down from the surface. The ancients being as smart, if not as knowledgeable, as we are today, there were certainly some who may have deduced the likely extensions of already known seams, and taken some shortcuts.
Here is a link on some ancient Greek and Roman mining methods, and here is one on ancient Egyptian gold-mining techniques. Note the similarities of the latter to panning during the California gold rush 2000 years later.
Details of historic prospecting can be found here.
Googling "ancient mining" and "ancient prospecting" yield additional references.
The Map that Changed the World by Simon Winchester outlines the quest by William (Strata) Smith, from 1793 to 1815, to prepare the first map of geological strata, for the United Kingdom, and lay the foundations of modern geology. William Smith is believed to be the first person to recognize, and study, the geological significance of sedimentary deposition of rocks. On Page 75 of the book, Winchester quote from Smith's diary in regards to the belief of the colliers that the evident and well known patterns of the coal mines did not exist in general:
I was told there was "nothing regular above the Red Ground", which in their sinkings varied much in thickness. Tis did not deter me from pursuing my own thoughts upon this subject.
The "Red Ground" was the sedimentary deposition above the Carboniferous Uncomformity in Somerset, where Smith warked at the time, and indeed much if not all of Britain and Western Europe.
Although the nascent science of geology existed prior to Smith's work, and the stratification of sedimentary deposits had been observed by others, the conclusions reached by earlier geologists were often bizarrely incorrect, by modern terms, and thus of no particular use in predicting the behaviour, existence, and location of buried strata.