Can you use Sugar beet sugar to make mollases - Yes.
Will it taste like Mollases Rum - Not exactly, with a few small nueacnes that most unrefined pallates will barely notice.
Will it tase good - Yes, but with a slightly different character, aging will only intensify this non rum like taste. But will be a good rum-like taste.
Thats why plane sugar has that unexplainable "citrus" taste to it when used to make Rum as opposed to using Blackstrap or regular unsulffered Mollases. Not sure right now of the exact %, but I know more then 75% of all generic store bought sugar is beet sugar currently. Unless it says "pure cane sugar" then you can bet you ass it's beet sugar. Why? Cuz beets are cheap, easy to grow in the US (and anywhere for that matter) and are very easy to process to extract the high sugar content. - where Sugar Cane is not.
Heres why: sugar is not always the "same" as every other sugar. Loosely translated as; Dextrose, Maltose, Lactose, and Sucrose are all made up of ROUGHLY the same componds, just rearanged in special forms. The make up and ratio of these chemical bonds, along with other "hitchhiker" elements, minerals, and nutrients are what are the basis for your wash. Once you distill them the ethanol that is produced transfers those chemical compounds with it and thats where you get the flavors from. Just like flavored salts, its the additives that make Fleur de Sel, different from Hawaiin Pink Salt. NaCl is always, and Will always be NaCal (salt) but the way the crystals are formed, the minerals that are bound to the outside of the compound are what flavor it.
Note: This is a laymens generalization based on the findinds and readings from "What Einstien Told his Cook" by Harold McGee and every science, chemestry class I have taken. I am not by any means a Scientist or chemist, just a Chef with a better then average palate. Mind you I will probably read this tomorrow and think WTF was I thinking... but hey! What is alcohol for?
As far as your troble with finding a suitable rum producing molasses; Try here:
and search for "Molasses" - The Unsulffered is what you are looking for.
Or if you want to use Corn Sugar (Dextrose) Try here.
If you want less then 5G (22.5L) then try looking up "Brear Rabbit" Molasses or one of the other types of unsulffered molasses from the US. I'm sure you can find something from the states that will meet your needs.
DAMN LONG ASS POSTS!!!