Nothing prevents them from demanding dollars or coconuts.
If they were to publish in pesos,the price would be outdated by the time the add is printed.
This is not a new practice, it is common for most foreign products. Only the dollars are slightly harder to come by.
Prices will "drop" in the sense that less pesos will show up over the table and more dollars will flow under. Parallel economy will adjust to this making it's own set of rules on the go. Inflation will thrive.