Short answer: No.

The Main Left/Right Outputs are considered the System Outputs. They include the System Effects (Rev/Cho which are accessed by each Part via a Send/Return type setup), the Master Effect, and the Master EQ.
The Assignable Left/Right Outputs are like direct outputs. They include the Voice and its Insert Effect. The purpose of the Assignable (direct) Output is to isolate a Part or Parts that you want to record or process separately.

The SYSTEM EFFECTS can be understood as communal effects. Each channel of the ES mixer has two Aux Sends: Reverb and Chorus (time delays). Think REVERB. You can send a little bit of the piano, a little bit of the lead synth, a little of the guitar, the snare drum, etc. using the Send Amount to determine what goes to the reverb chamber... In the chamber you have all these signals bouncing around... There is a combining amp that Returns a composite of all these instruments, now "wet" with effect, to the main L/R output. This is much how effects work on any mixer.

The assignable or direct out take the signal and routes away (in isolation) so the direct assignment is "pre" the Aux Sends, and anything assigned to the assignable outputs is completely removed from the System outputs (for that reason). The purpose is NOT an additional Main output, the purpose is to allow direct or isolation of signal.

The System Effects are like a public communal "pool"... All signals routed in get "wet", all "wet" signal is Returned to the main L/R output just prior to the Master Effect and Master EQ