Trivially, yes. If the landmass is small enough, it can easily be controlled by a single empire.
However, that's not a very interesting answer, so a better question is how big the landmass could be. We can use real-life examples to see how large this hypothetical controllable landmass is:
0-1,000,000 sq. km of land: Easily. According to the sizes listed here, countries today range in size from <1 square kilometer (Vatican City) to more than 1,000,000 sq. km(Russia). The average country in the world takes up about 750,000 sq. km, which is about the size of Chile and Turkey. The Byzantine Empire roughly covered Turkey back in the 9th century, so these sizes are definitely possible.
1,000,000-15,000,000 sq. km of land: Probably. According to this list, there are plenty of large empires in history. Rome, Alexander's Macedon, and the Ottomans all claimed about 5 million sq. km of contiguous land at their peak, the Umayyad Caliphate got to about 11 million sq. km, and the Qing dynasty of China reached about 15 million sq. kilometers, which is about a third of Asia. These empires are certainly at the technological level you described, and there are plenty of examples so this size is pretty doable.
15,000,000-25,000,000 sq. km of land: Possibly. There are two historical land empires in this category: the Russian Empire and the Mongol Empire. The Russian Empire formed in the early 1700's so it might be a bit too advanced compared to the examples you gave, however the Mongols are the interesting one here anyway. At it's peak in the late 13th/early 14th century, the Mongol Empire covered 24 million square kilometers of land. This is about the size of North America. Since this is the largest land empire in history, it may be around the upper limit for the size of empire at the technological level of your examples.
25,000,000+ sq. km: Probably not. The largest empire in history, the British Empire, controlled about 35 million sq. km at it's peak. However, they cheated and used boats, which significantly sped up their empire-wide communication and logistics. Since no other empire has come close to this size, it is unlikely that an empire could come to this size without significant use of the ocean around the supercontinent. This would also require the continent to be thin or fjord-y in order to let ships cover most of the travel distance.
So, an empire easily can control an entire landmass: it's the size of the landmass that determines if some single empire can control it. According to real-life examples, a landmass the size of North America seems to be the upper limit for an empire with an ancient or medieval level of logistics ability, since nothing has gotten larger than that on Earth even though larger landmasses exist.