Is it okay to connect a round supply duct directly to an air handler?
Such a connection introduces more friction to the system, reducing the available flow. If the system is sized adequately to accommodate this, then yes, it is OK. If I understand you correctly, this large round duct you are connecting to the air handler is serving as an extended plenum. Partly depending on the relative size of the duct and air handler, this may be the one place where it would be worth constructing a proper transition fitting instead of a simple flat adapter.

In a way, the flat adapter is crippling the entire system before it even gets a chance to get going, just my opinion, based on my innate desire for efficiency. As stated earlier, if the system can accommodate an inefficient transition, then it is OK to use it. I just happen to not like it.