Can You Convert a Gas Log Set from One Gas Type to Another?

No.  The set has to be fitted for the correct gas type before shipping because in most cases the burner for each gas type is a completely different burner.  With grills or heaters, it's as simple as changing the orifice and the hose, but with a gas log set, it's asking for a completely new burner and fittings.  Due to where the holes are located and the permanent nature of welds, it's impossible to get to these places and expand or contract them for the different gas type.  Fortunately it's very unlikely that this conversion will be needed since gas log sets aren't very mobile.  A grill or a heater will probably come with you during a move, but the gas log set will likely remain in the fireplace it's installed in.  It's unlikely the gas system of a house or building will change from one type to another as well.  Unfortunately if you do find yourself needing to have a propane set changed to natural gas or vice versa, all you can do is buy a new burner kit and lighting control.  It might be inconvenient, but there's no real way around it now or in the foreseeable future.