ok, i just did some tests in Blender's cloth sim.  what i'm seeing is this:

• if you want structure, edge loops are helpful.   just putting a nice dividing line between two different topologies gave it a little more structure and made it more likely to bend there.
• tris might be better in general, but so far i'm not seeing much difference at all with a basic plane draped  on a sphere at what i'd consider medium resolution polys.  certainly not enough to be more of a concern than generally good topology.
• i used a command i hadn't noticed before called "Flip Triangle Edges" to make the topology more random and break up the grid on half of my plane.  it really changed the behavior.  not necessarily improved it, but changed it.  it made it crumple a lot more. which is great for, say, silk, but awful for say, denim.  in Poser you can control this with Sheer settings, but this will undercut it.

it's definitely not scientific, but i'd say it's still better to model in quads and control topology for structure, convert to tris if it won't kill your poly count and making running a sim a pain, and use some sort of randomizing method only if you want lots of bending and crumpling.