Hi, I guess that you are talking about solenoid injectors fitted to a common rail diesel?
If this is the case, then typically there is no problem with disconnecting this type of injector, but as Nige stages the capacitor discharges it's 80v which could cause a problem within the ECU.
I have seen cases where a long term open circuit injector corrupted the memory within an ECU, specifically the immobiliser, leading to a non start condition.
One reason for diaconnecting an injector whilst the engine is running is to determin a missing cylinder. If you use the pico high amps clamp you can do a relative cranking test (depending on the use knock the inertia switch, unplug the pressure regulator or cam sensor to prevent the engine from starting). This will help illustrate any mechaincal faults.
You can use pressure regulation percentage and the pressure sensor voltage, or serial data (injection correction) or the current clamp (injector pulse width variation) to indicate pressure drop through faulty injectors. Final confirmation can be achieved with an injector leakoff test.
We cover these procedures (using Pico) on our one day Common Rail Diesel training courses.