Normally, if only the connection labeled Left/MONO is used (nothing connected to the Right output), then yes the mixer combines L/R to that one output.
YMMV, not knowing the mixer being used, but that is normal behavior for a lot of mixers, especially if labeled that way.

Some older ones may require a MONO setting elsewhere on the mixer. Often a simple button.

Test it and see if you can hear an instrument panned hard right through the speaker ...

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