You should send a message to "c4c5specialist" about this. He's the resident "chief surgeon" and he should have the answer.
My guess is that IF you have the receiver and IF the BCM has the correct RPO codes for it, then at the very least you should be able to buy a FOB (up to three, actually) and program them to work. But it might not be completely good news.
Lets say that 1) you've got the required recv'r installed and 2) the BCM has the codes. Did the RHD conversion include rewiring the doors? If not, when you press the UNLOCK button on the remote, will it open the passenger door (left door) first? and the drivers door (now on the right) only after the second UNLOCK press?
That may the worst of it, provided you've got the rec'r and the BCM codes, something you may have to live with unless you do some major surgury on the wiring harnesses.
The receiver is located up under the left side of the cargo area above the rear-left wheel housing. You'd have to pull off the left interior trim piece to get at it. It looks like a cigarette box sized box with a rod-like antennae protruding from both front and back running along the inside of rear left quarter panel. If the receiver is there, you could then test the BCM for the presence of the correct RPO codes by starting to do the FOB reprogram procedure, but stop after step #6:
[this is straight from the 2002 Corvette Service Manual. Vol. 3]
1. Turn the ignition to ON
2. Turn the radio to OFF
3. Press the RESET button on the Driver Information Center (DIC) in order to clear any IPC warning messages.
4. Press and release the OPTIONS button on the DIC to scroll through the display options unitl the IPC display is BLANK
5. Press and hold the RESET button 3 seconds
6. Press the OPTIONS button until FOB TRAINING message is displayed.
{If you see FOB TRAINING then the BCM has the correct RPO codes and you should be OK to just buy a FOB, Program it using steps 1 thru 6 above + steps 7 and 8 below.
IF FOB TRAINING cannot be displayed, the BCM doesn't have the RPO codes and would have to be reprogrammed. I can't help you with that, sorry. You should just turn OFF the Ignition at this point to exit the programming mode.}
7. Press the RESET button in order to begin the programming sequence. The message HOLD LK + UNLK 1ST FOB will be displayed
8. Simultaneously press and hold the LOCK and UNLOCK buttons on the first transmitter for 15 seconds. The IPC will indicate when that transmitter is programmed and when to procede to the next. Repeat this procedure for each additional transmitter or press OPTIONS button to exit.
Again, you should contact c4c5specialist here on the CAC to get a better idea of what would actually be involved.
Cheers