Most (low cost at least) fab houses make holes plated unless directed otherwise (and sometimes at extra cost for non-plated holes). The plating in the hole depends on the copper layers on each side to anchor it in place, particularly during the fabrication process. If a hole is plated without a pad on each side, the plating can come loose during processing and end up shorting tracks together on the finished board.
Holes are plated to make a connection between the copper layers and to allow a better solder connection to be made.
Where would you want non-plated holes? Board mounting holes might be non-plated, as might mounting holes for switches.
Board fab houses may want a Gerber layer called NPTH to identify non-plated holes. These holes are physically plugged when holes are plated. It's an extra step in the boards making process.