No, not always, because even when coins are made of precious metal there are other values coins represent that can't be so easily exchanged.

I'm just going to look at Greek for this comment. China has coinage as old, but it works on very different principles of manufacture and I don't know enough about the cultural stuff to make useful comments. I also don't do modern stuff.

One thing coinage, as opposed to just bits of metal, does for someone is provide an easy way to guess the metal content of the coin. Athens, to just pick a city, might strike a drachma of a consistent weight (they might not also, but for now let's just assume they do), and the user can have confidence in the weight of the Attic drachm without bothering to weigh every coin. Rhodes might also strike a drachma of a consistent weight, as was the case with Athens, but if the weight standard is different (Attic drachma is about 4.3 grams, the Rhodian drachma is about 3.7g) it is difficult to make change.

The differences in weight standard could be exploited by the state. Ptolemaic Egypt used a tariffed drachma; it was lighter than the Attic drachma, but the only legal currency in Egypt, and the state exchanged it at 1:1, so the state made silver every time someone came to Egypt to trade.

There is also an ideological component. The most extreme example I know is the Libyan coinage of the Mercenary War (just after Punic 1). Carthage's mercenaries, when Carthage didn't pay them, revolted, along with Carthage's Libyan allies, and struck a series of coins in an alloy of copper and arsenic of all things. The arsenic makes the copper look like silver. They look like shekels to to all the world, stamped with the ethnic "Libyon" ("of the Libyans"), and would have been completely worthless in another context, but they left hoards, so someone was using them....

There is also countermarking, which is a practice in which a coin struck by one authority is remarked, indicating it is approved by another authority. People might do that for different reasons, but I think it's ok to say it's a sign that there is some element of the value of the coin aside from its weight and ease of conversion or making change.

Coinage worked differently in ancient times than today. Most coins used in trade were made of silver, gold, or electrum, which gave them a value that was widespread. A five dollar bill won't buy you much of anything on the streets of Paris, but silver is silver everywhere.

One of the reasons that official coinage developed was as a way of certifying weight and purity of precious metal. The head of Athena and the owl stamped on a piece of silver certified that the city of Athens stood behind that coin as having, for example, 4 drachmas worth of silver.

As with all forms of coinage, the degree to which people in other places recognized foreign coinage depended a lot on who was offering it, who was receiving it, and which coinage it was. A city-state like Athens produced voluminous coinage that was well known through the Mediterranean and beyond. Merchants knew what they were supposed to look like and weigh. Those coins today are found all over Europe and the near east, which would certainly indicate that people well outside Athens had no trouble using them. The same is true for other ancient cities such as Syracuse, Corinth, and Tyre. (Tyrian shekels were desired enough that it was the only way for the Jews of antiquity to pay their temple tax. The 30 pieces of silver paid to Judas in the New Testament were almost certainly these coins.)

Sometimes governments took advantage of the general acceptance of certain coins. For a century or more after the death of Alexander the Great, many cities and kingdoms were still minting coins in the same style as Alexander had, with a lion skin clad head of Herakles on the obverse and Alexander's name and title on the reverse. Celtic tribes minted coins in imitation of Rome.

Certainly, if you had been a trader landing at Syracuse with a purse full of Athenian tetradrachms, you might expect to need to have those coins weighed by anyone you wished to spend them with, but it might have been easier to use foreign money then than it is today.