There is no evidence in ancient sources that indicate that salt was used as a currency in Rome.

Occasionally an incorrect translation of Pliny's Natural History 31.89 surfaces that claims he says this, when in fact he says that salt:

is also related to magistracies and duty abroad, and that’s where we get the word ‘salaries’

Which is a typical Roman etymological explanation.

Livy 29.37.3 talks about the imposition of a salt tax c. 200 BCE and it is possible, I suppose, that this was used for military purposes.

Salt simply wasn't that valuable and the Romans had good supply routes to abundant sources

Down river from Rome at Ostia there are salt marshes, which from Rome's earliest days and even earlier were exploited for salt. The process is the same as sea salt harvesters use today. Harvesters arrange large flat pools surrounded by walk ways and little gates to let sea water in. Let water evaporate under the sun so that salt crystals precipitate to the bottom. Let in more water. Repeat until there is enough salt to rake into piles and gather for export. The Via Salaria, so called Salt Road let traders carry the stuff from Rome into the mountains where salt was harder to come by and was valued as a preservative for meat and for making cheese. (By the shore it could preserve fish.)

The salt/salary thing, as skimitar notes, is folk etymology; the Romans had a lot of that sort of thing, and this one is such a good story, it has lasted to this day. But salt was never anything more than a commodity, valuable, but not a means of exchange. People expected to be paid in bronze, silver and gold. The failure of Roman silver and gold reserves to keep up with demand and the catastrophic debasement of silver currency with lead is one reason for the decline of the empire. By the end, soldiers demanded and got payment in gold.

But that's another story

(See Kiwi hellenist for the long read re salary)

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In regards to boiling seawater for salt, there a couple answers explaining how impractical it is to amass and sell.

u/wcspaz and u/AncientHistory answering https://www.reddit.com/r/AskHistorians/comments/4kz3le/im_given_to_understand_that_in_the_premodern/

u/Lynx_Rufus answering https://www.reddit.com/r/AskHistorians/comments/5opntw/why_was_salt_so_scarce_and_valuable_when_it_is_in/