I was watching gladiator with my brother during the coliseum scene of 2nd punic war (Hannibal vs Scipio). The man announcing just projected his voice across the whole coliseum. It didn't seem accurrate to me but what do I know?
edit: I didn't think there'd be this much interest. Its funny how the posts you forget about are the ones that blow up.
There are a couple of main categories of pre-amplification public speaking: fixed public speaking, in which the speaker is in an architectural space designed for such an activity; and field public speaking such as on a battlefield or other uncontrolled space.
In both categories, as others have mentioned here, people who needed to be heard over large spaces (actors and performers, statesmen, etc.) trained their voices to learn volume and projection. Part of a Greek's education in rhetoric included not only philosophy and the formulation of arguments, but the physical skills of vocal projection. (The Greek orator Demosthenes famously was said to treat his speech impediment by putting pebbles in his mouth and shouting above the roar of the ocean.)
There is little controversy about the nature of fixed public speaking because we have architectural remnants and records that show spaces (e.g., amphitheaters) designed specifically for spoken-word performances and project the sound of the speakers or singers. Ancient Greek theaters such as the Theater of Dionysus in Athens held up to 17,000 people, and structures such as the Theatre of Epidaurus indicate that the acoustic engineering of these spaces was well understood. Similarly, minarets on mosques, through a combination of their height and the shape of the dome or cone on top, are designed to use architecture to amplify the call to prayer.
Even today, many people study the design of these ancient acoustic spaces, they can be extremely sophisticated. (For contemporary research and interpretations, check out the Acoustical Society of America.)
In these specially designed structures, a trained performer orating at a volume of 90dB (very loud speech) could be clearly heard by everyone in the space. People perhaps less trained in vocal projection (e.g., a non-performer using the space for a public meeting) could also use simple megaphones, either hand-held or wearable (by which a small megaphone is built into a mask the speaker wears).
A reminder that even today, performers in spaces such as the Metropolitan Opera in New York are not electronically amplified. Of course they have a high level of special training, but their performances can easily be 100dB and clearly audible to everyone in the theater.
There is significantly more controversy around field public speaking, its methodologies, and the accuracy of written accounts. In short, there isn't solid agreement in archaeoacoustics (yes, that's a thing) about whether or not a military leader in the field could successfully address a large group given the potentially chaotic environment, if such speeches were relayed by others like a phone tree, or if the same speech was given multiple times in different locations. A lot of researchers have attempted to test via re-creations, detailed scientific acoustic analyses, and other academic techniques, but it seems that historians remain divided. (See Hansen, "The Battle Exhortation in Ancient Historiography: Fact or Fiction?")
There are sufficient examples of ancient megaphones across various cultures (we have megaphone artifacts all over Europe, and also in North America and Asia) to indicate that this kind of field public speaking was engaged in, but we have little reliable information on how effective it was in various circumstances.
One interesting anecdote of note, however, comes from Benjamin Franklin: He disbelieved the reported crowd sizes allegedly drawn by famous preacher George Whitefield until he attended one in person and did a quick calculation of those present. He concluded that the crowd was more than 30,000 people (actually a lot more), and that Whitefield's booming voice was intelligible to the majority of those in attendance. (See Thomas Kidd, "George Whitefield: America’s Spiritual Founding Father").
And anyone reading this far should also see u/IPikrates answer in the FAQ about rousing pre-battle speeches.
More precisely to your question:
The Second Punic Wars, (218 BC – 201 BC) were 60 years before Mummius, the victorious Roman general and consul of 146 BCE transported acoustic devices and architecture from the Greeks to Rome after the battle at Isthmus of Corinth. And according to Vitruvius, probably the most well-known architect and civil engineer at the time, those acoustic innovations were not implemented anywhere for decades later.
So your speech in question, if it occurred at all, would have taken place many years before the Romans had adopted superior acoustic engineering for public speaking. (And the Colosseum was not completed until 80 AD, so it could not have occurred there.)
But even so, given examples like Whitefield, a sufficiently trained and booming voice might carry in an enclosed space such that the majority of a large crowd (such as the Colosseum's 50,000) could understand him. It's not an outrageous possibility, and certainly forgivable to include in a work of fiction like Gladiator.
References:
More of course can be said, but we do have some older threads about this topic which will be of interest. I'd recommend you check out this thread by /u/iphikrates or else this one by /u/Celebreth.