Hi Avery,
Back in the days when Serial ports in PC,s were implemented on an ISA card you knew what you were dealing with. You could identify the serial driver chips and replace them if you blew it up.
Now that all the serial ports (if you have one) are done in highly integrated port chips on the mother board you usually get less voltage and current from them and if you blow it up you need a new motherboard or try to find a card type one to fix your PC.
So the answer is. Yes, it works but how well depends on the drive capability of the driver involved and whether you can arrange for RTS and DTR to be at logic 0 to share the load.
Perhaps the USB solution is already the best solution??? At least you have a reasonably known quantity here. Although be also wary that virtually none of the "el cheapo" add on devices support the USB2 high speed standard in so far as current output is concerned.