Can vias and traces conduct electricity on PCB surface?
If the board does not have solder mask covering the tracks, then any metal or other conductive material placed on the board may contact the tracks and cause a short.  Even with solder mask, you should have some additional insulation between conductive material and the board.

In most CAD programs, you can define "keep out" areas when you build a footprint, so that the Design Rules Check function of the PC layout program will warn you if you place tracks where you shouldn't (or even prevent you from placing those tracks.)