Acid + carbonate –> salt + water + CO2
What they’re making will only contain one ingredient or the other in much reduced quantity, plus some water, plus some dissolved rubbish. It’ll fizz for a bit though. If they get the proportions bang-on, it’ll contain none of the initial ingredients at all.
If you’re going to critique the chemistry, at least read the whole sentence you’re critiquing……
“making sodium citrate solution. sodium citrate is still an emulsifier but I’ve no idea if it’s more or less effective than the individual ingredients.”
It’s a common ingredient in soap, although google suggests it’s more to prevent watermarks and soap scum than for it’s properties as a surfactant itself.