If you are pumping the primer and it's going straight into the crankcase from the injector, then it can be assumed that the injector has failed.
In reference to your question on removing the injector while still hooked up.....Yes, it can be done, although it's not real easy.
What would that benefit of that anyway?
The new injectors come with new moulded nitrile fuel hoses in the kit.
This is because of newer epa regulations, which state that: any hose broken lose or removed must be replaced with new hose. In addition; any constantly wetted fuel in a hose needs to be of a non permeable designed nitrile fuel hose.
This unfortunately equates to increased cost.
The TS500i differs from a M-tronic in that it has a computer that stores failure codes and "remembers" it's last settings.
It is also quite a bit more complex, in that it is a fully injected system.
If you change a defective part, I've found that although they may run without recalibration, it seems to much longer for the saw to behave as normal, and may not idle well (if at all) until used a while.
I'm not sure why, but IMO; huge adjustments to mixture seem to take time for this system to cope with and adjust to, and thus the need for recalibration.
The recalibration is necessary when a component is replaced that was causing problems; like a really plugged air or fuel filer, injector, bad seal, etc.
That way it will start and idle great, right out of the gate.
The fine tuning happens automatcally during operation.