Is it feasible for the Roman Empire to experience an agricultural revolution similar to that which Britain went through in the 15th to 17th Century? How much of a population boom could this have caused? What would the effects have been?
No (filler)
Agreed.
You could, however, probably get the Romans to adopt mideaval agriculture techniques and that would cause population growth
To adopt medieval agricultural practice you would need first to develop the heavy plough, and that would demand that the blast furnace was developed. Also to get the true benefit of medieval farming you would need red clover to spread, and at the time red clover had not been trough the radical selection, which made it a grow faster than the native wild clover of Europe, plus you wouldn't get the full benefit without three or four field crop rotation.
Mildly put you simply need several difference developments to see a Roman agricultural revolution.
Of course you could start with a milder one, where we start with introducing three or four field crop rotation together with peas (peas fixtate nitrate into the soil, through less efficient than red clover, it was usual used together with four field rotation). You could also push the development of the heavy plough with a few centuries. The primary problem is that this just mean that Germanic population will be even greater, as these improvements will be primary a benefit north of the alps.
If Germans can farm the land where the trees are growing, they will clear the forests and their wives will have more babies and more of their children will survive to adulthood and so on and so on. The same will be true of the Slavic Venedae and of the Finnic peoples even further away.
The Romans certainly could have learned to build blast furnaces. The Romans built in cement, after all. But now you have me wondering if once the shape of a moldboard plow was well known, if a plow could be molded with cement or concrete (cement and gravel) reinforced with wire and then, after it hardened, a thin, red hot layer of iron hammered onto it and riveted into place. Or the same done with wood which is then quenched the way an iron rim is put on a wagon wheel. There's lots of ways to stretch iron if iron is expensive.
So yes, I think the IDEA of a moldboard plow, which parts the earth inversely to the way the prow of a ship parts the waves, could have caught on a lo sooner than it did. And if it had, Rome would have had quite a few more civilized and prosperous neighbors than it did. And a lot more competition.
We shouldn't forget that the British Agricultural Revolution took place well after the exchange of crop package that occurred with the discovery of the New World.