I don't think that this has any historical basis. This account is based on Gibbon's Decline and Fall of the Roman Empire, a book from the eighteenth century and rarely a reliable guide to Roman history nowadays. All the more so in this case since there are no footnotes for this incident, so it is impossible for the reader to know where the story is from.

A bit of digging reveals that this was from Eutychius' Chronicle from the tenth century. I can't read Arabic, but a translation has been kindly made available by Roger Pearse:

When Heraclius began to reign at Constantinople, he was engaged for six years in a violent siege. Exhausted by the siege, the inhabitants of Constantinople, many of whom had already died from hunger, decided to open [the gate of the city of] Constantinople to Kisra. Learning of this, Heraclius was afraid that they would open the gate and hand him over to Kisra. So he sent to Kisra saying: “I’ll give you anything you want as long as you leave me alone.” Kisra wrote him saying: “If you want me to leave you in peace, pledge to send as your ransom, and for the city, a thousand qintār of gold and a thousand qintār of silver, a thousand virgin maidens, a thousand horses and a thousand heads of embroidered silk. This ransom you will give to me every year, I will stay away and I’ll leave you alone. Send me immediately the ransom for this year, and do not postpone it, if you want me to leave you alone.”

Heraclius wrote to him: “I consent to what the merciful king is asking of me; at the moment, though, I do not possess all the ransom money, for the merciful king has not permitted me to do whatever I wanted. But if the merciful king will give me the opportunity to go out, I will gather the money and everything else required of me. I will send you everything in six months, if the king will wait for me, and will allow me to go undisturbed around the villages in order to collect the goods for which he has asked me and so satisfy him.” Kisra granted this request. So Heraclius gathered his ministers and generals and told them: “I have only placated Kisra in order to calm him, and inspire confidence in his men. In truth I’m going to travel to Persia. I am certain that Jesus Christ, our Lord, will give me the victory over the Persians, and so we will get rid of Kisra and his men. If I am late and do not return at the end of six months, make sure to keep Kisra in suspense, filled with promises and defer throughout the year your commitment to give him what he requested. If I don’t come back, or not come back to you, do what you please. I leave my brother Constantine as my successor. Do you accept what I’ve said to you?” They accepted and wished him victory.

From this, it is abundantly clear that Eutychius had muddled up the events of the Roman-Persian War of 603-28. Constantinople was besieged, but only in 626 (by the Avars rather than the Perians). Heraclius did offer humiliating terms of surrender to the Persians, but in 615, and his offensives into Persian territories only started in 622. Moreover, Heraclius did not have a brother named Constantine, but he did have a son named Heraclius New Constantine, so evidently another wire got crossed there. Given the gap between Heraclius and Eutychius, I think that it's quite understandable why this confusion occurred - especially as the seventh century was chronicled only sporadically by contemporary sources and the most useful accounts are the Greek Paschal Chronicle and an anonymous Armenian history now attributed to Sebeos, neither of which would have been likely to be available to Eutychius in Egypt.

Still, I'd like to think that Eutychius did the best job he could in the circumstances. A Persian army did stand at Chalcedon in 615, literally only one sea-crossing away from Constantinople, and in these circumstances Heraclius did try to make peace:

We beg your Clemency to hold our most pious Emperor Heraclius as (your) genuine child, for he eagerly wishes to do the service of your Serenity in all things. In doing this, you gain a double glory for yourself, both for your valour in wars and for the gift of peace. And henceforth we shall enjoy peace through your eternally remembered gifts, taking the opportunity to offer prayers to God on behalf of your long good health, and holding your good deed in remembrance through the ages of the Roman state.

In short, Heraclius conceded the Persians' overlordship over the Romans, turning the traditional Roman worldview completely upside down. Khusro in fact rejected this offer and the war continued, a particularly dramatic moment being the fall of Alexandria in 619. Having carefully shepherded his resources for years, Heraclius went on the offensive in the Caucausian mountains, campaigns that were reported by Eutychius after the passage discussed here. These campaigns were surprisingly successful and he did indeed threaten the Persian heartland, even their capital Ctesiphon in 627. Yet Eutychius conflated these offensives into a very short span of time, with Heraclius having 'destroyed' the Persian capital by the 'seventh year' of his reign - Heraclius did not destroy Ctesiphon even in 627 (the seventeenth year of his reign), but he got close and as a result the Persian court panicked, culminating in the downfall and execution of Khusro II.

As for the terms of the fictional treaty, I see some similarity with other treaties recorded between the Romans and the Arabs during their wars in the following decades (one example that comes to mind is the 'daily tribute of 1000 gold coins, one horse and one slave' recorded by Theophanes the Confessor), but I am not a military historian and do not know of how historians view the actual logistics involved (or if these accounts can be seen as anywhere close to being representative of reality).

TL;DR - it didn't happen.