Yes.
It starting instantly indicates the charging system-battery is probably OK.
Sounds like cylinder(s) not firing/missing. You might try pulling plug wires one at a time while it is idling and listen for any that do not change the sound of the engine.
A good test to perform while it is forcing you to hold it at high idle to keep it running too.
The air metering plate (where the air cleaner/breather leads to)....If it dies and you immediately switch it off, no resistance when you press down on the plate would indicate a a loss of fuel pressure (bad filter, pump, restriction, etc).