The answer to your question is possibly less clear than you might think.
As far as Eagle is concerned, a PTH pad (the type with a hole!) is assumed to be plated through. It has a copper ring on all layers, connected to the through plating. A hole, on the other hand, defines no copper at all, and actually creates and exclusion zone to ensure traces can't approach too closely. These are assumed not to be plated.
However, when you get your board fabricated, you are (probably, depending on the fab house) sending only generated Gerber files. These do not include anything that (explicitly) distinguishes between holes and pads. Many board houses will use some form of heuristic - probably as simple as "if there's copper over the hole then it's plated" (note that the Gerber files for layers don't show the holes - they're in the Excellon drill file - so the pads are filled). Some board houses, however, will through plate all holes. If there's no annular ring, then this plating has no electrical connection to anything, so it's harmless. Alternatively, you may find you need to give them a list of drill sizes to leave unplated (mounting holes tend to be a different size to any of your pads). You need to check with your board house.
