Can the RCX connect to infra-red on a computer?
As far as I remember, the protocol LEGO uses is incompatible with standard IR protocols used in PCs (not even the same frequency, if I remember correctly).

The NQC FAQ has some more explanation on why it's not possible, but their short explanation says it all:


  Quite simply, these protocols are incompatable. (sic)


You may have some success using a NXT brick and the IRLink sensor, but I'm not sure how far you can go (for example, I'm not even sure you can upload a firmware, and you need to be able to do that).

The easiest way is to stick with the IR tower, and in addition of the serial-to-usb converter mentionned by Zhaph, don't forget there's a USB version of the IR tower available on Bricklink (see here or here).