Can I install A/C in a home built in 1924 which has round heat ducts in the ceiling?
Sure -- or at least, there's nothing about having round ducts in the attic that would make A/C installation more difficult. In fact, because cold air is more dense than warm air, ceiling vents are usually considered better for cooling. The cool air flows down from the ceiling, helping ensure your rooms are evenly cooled. That's why many houses in warm climates tend to have vents in or near the ceiling. And why vents are typically low in colder climates.

If there is reason for concern here it's about the heating, not cooling. Is the attic space insulated? If not, then your ducts are going to lose heat in the uninsulated attic space, and the home will cost more to heat. This can be mitigated by good insulation &amp; sealing around the ducts and vents. Secondly, assuming your vents go through the ceiling, there is also some additional heat loss through these ceiling penetrations. And finally, because the vents will need to blow heat down, they might not do as good a job at making your whole house feel evenly heated when it's cold outside (because hot air rises, but the vents are already up high).

None of this is a deal-breaker, though - just different design tradeoffs. If you want to evaluate the bottom line, ask for a few months' heating bills so you know what to expect. But also know that factors like good air sealing, attic insulation, windows, and an efficient furnace will make more of a difference than whether the ductwork is in the attic or basement.