Yes, Roman treaties (maybe all treaties in the ancient world, but I'm not comfortable making that claim) would have a religious element to make them binding. Slight topic detour: I think it would be a mistake to see this as an impractical or mystical element--after all, in the contemporary US someone swears an oath on a Bible before testifying, which doesn't mean there are no perjury laws. More importantly, oath breaking and oath keeping tended to be discussed in the language of personal honor rather than divine punishment--Brutus was tormented about his personal sense of honor, not visions of divine punishment. Anyway.

In Polybius' Histories he described four treaties between Rome and Carthage, and at the end appends a note on the manner of oath swearing:

Provision was also made for swearing to these treaties. In the case of the first, the Carthaginians were to swear by the gods of their ancestors, the Romans by Jupiter Lapis, in accordance with an ancient custom; in the case of the last treaty, by Mars and Quirinus.

The form of swearing by Jupiter Lapis was this. The commissioner for swearing to the treaty took a stone in his hand, and, having taken the oath in the name of his country, added these words, "If I abide by this oath may he bless me; but if I do otherwise in thought or act, may all others be kept safe each in his own country, under his own laws, in enjoyment of his own goods, household gods, and tombs,—may I alone be cast out, even as this stone is now." And having uttered these words he throws the stone from his hand.

A very interesting example of ancient treaties that survive in their original form are the Pyrgi Tablets, a bilingual text recording an agreement in Phoencian and Etruscan. You can read the text here, where you can see that the text was adapted to the different religions of the different parties.

When studying the Romans it is very challenging to separate religious and political aspects from each other, the two were nearly completely interlinked. The Romans wrote treaties and while doing so would invoke their gods to punish them if they broke them to add sanctity to their actions. So when they declared war they would do so cloaked in ritual to give them additional legitimacy.

There was a priestly college called the fetailes that were devoted to Jupiter and were responsible for diplomacy including declarations of peace and war. Livy wrote that the fetial would approach the boundary of a foreign city, covers his head in wool and then makes a list of demands that Rome wanted. Then he repeats it when he crosses into their territory, again to the first person he sees, again to the city gates and then again in the market place. He then waits 33 days and if the demands are not met he returns to Rome where he presents his findings to the king or senate depending on the period. If they find that war is now the best course of action he returns to the territory with witnesses and ritually throws a spear into their territory declaring war.

One interesting facet of this ritual is that as Rome grew it became harder and more unrealistic to send fetiales to other nations so they came up with a work around. While fighting Pyyrhus the Romans were unable to land a fetial to complete the ritual so they captured a soldier, made him buy land in the Circus Flaminius so that it could be considered foreign territory and cast their spear into it.