There’s only one way to find out!
Unaged rum, there’s Prichard’s Crystal White and Wray & Nephew White Overproofed. I’m sure there are others, but those are the ones I know.
Failing that, white cachaca is essentially unaged rum, though you may have more difficulty finding that than the actual unaged rum.
(Yes, I am aware that cachaca and rum are technically not the same thing, usually, but for this type of experiment I can’t see how it would really make any difference)
I too encourage any experimentation in making booze. If you truly want to start with unaged rum, don’t just reach for any clear rum. Many of them (like Bacardi Silver and Don Q Cristal) are aged in barrels for while, then carbon-filtered to remove color.
As for the barrel, there’s not really something magical about reusing whiskey barrels. The reason so many rum makers do it is because some whiskeys must be aged in new barrels, so there are used barrels available. You might get a little a different character in the rum depending on what was previously in the barrel (especially for something like cognac or sherry), but you’ll have a much easier time finding oak chips at your homebrew show than finding a barrel to chop up.
Bourbon distillers can by law, only use new charred oak barrels. So every time they empty a barrel, they can’t reuse it for bourbon. So they sell them to Scotch distillers, rum distillers, etc… The thing is, once a barrel has been used for bourbon, the wood character is drastically lessened; I’ve had Scotch distillate (white dog) aged as if it was Bourbon (4 years in a new charred oak barrel). If I had to describe it, it was 90% Bourbon, 10% Scotch in flavor. The flip side is that a HUGE component of Bourbon flavor is from the barrel, which is probably what you’re getting in your ghetto whiskey.
The barrel plays a bigger role than merely being made of wood and toasted. There’s a gradual loss of whiskey to the outside wood, called the “angels’ share”, which concentrates the flavor of older barrels. Sometimes the really old ones are well less than half-full. There’s also some degree of something akin to carbon filtration going on with the charring- supposedly it adsorbs some degree of fusel oils, etc… as the whiskey ages.
So in a sense, you’re getting the barrel flavor, but none of the benefits of aging, I’d wager.
I seem to recall they made faux whiskey from medicinal alcohol in the movie Mr. Roberts. I don’t recall the ingredients they added, certainly didn’t sound like it would pass for the real stuff but maybe good enough for guys stuck on a ship in the Pacific. This website has this item:
“The Scotch preparation sequence is a small part of a fairly long scene. The liquor begins with grain alcohol. Coke adds color; iodine adds taste (taste? ugh); and the coal tar based hair tonic ages the mixture. It may have been lousy Scotch, but it did not contain vanilla extract!”
ETA: And here’s the clip.