Perhaps, if you heatsink the pins with some generous copper pours on the module side, and specify a sufficiently brief soldering profile, they won't melt out.
If the board is to be flush-mountable without any stacking height, that still wouldn't help much. Even with steel pins.
Other retention might be an option, too. Use a board-to-board header with zero solder tail length, extra stacking height (i.e., 10mm pin length + 1.6mm board thickness), and a plastic molding that rests on the PCB top side.
I don't think I've ever heard press-fit connectors recommended where reliability is desirable. One story I heard:
An FAE was in, bragging about their new so-and-so press-fit headers. Typical 99.7% connectivity rate! Engineer: "So, if I have a little backplane, with three of these 300-pin connectors on it, can you tell me where those three faulty pins are?" The meeting got suddenly quiet...
Mechanically/metallurgically speaking, I don't see why you wouldn't be able to / want to solder such a pin. If the press part comes loose, surely it's no less strong than a tight fitting soldered joint? Perhaps the assumption is, the insertion process destroys the barrel of the pad, weakening the solder joint?
It's generally not recommended to solder *crimped* terminals, but I believe that's more for fatigue reasons -- the joint itself is already more reliable than solder ("gas tight" bond, without using a soft filler that can fatigue and creep), but by adding solder, you inevitably cause the wire to stiffen, increasing fatigue stress on the wire at a little distance from the connection (assuming stranded wire, that is). In this case, I wouldn't think heat stress would be a player at all -- crimp lugs are made of the same material as the wire, so they both heat up and expand at the same rate (being conductive and all).
The same won't be true of PCB, as FR-4 has a much greater expansion rate, and the copper plating isn't there for strength (if it were, it would pull away from the board, readily!). But, having a metal-filled barrel obviously isn't a terrible hazard (soldering in leads and all), so...
Tim