Slightly possible, but not likely. This sounds more like a too lean air-fuel mixture. You'll need to bite the bullet and get the fuel presure gauge setup with the in line valve to find out what's going on. Trying to troubleshoot K-Jet without the gauge is like troubleshooting a modern fuel injection system without a scan tool and DMM; possible but difficult, and can lead you to replace good parts.

Now, it is possible to adjust the air-fuel mixture adjustment to give a good idle (assuming all else is OK), but if the control pressure is too far off, you'll just end up with a lack of top-end power because the air meter can't open up the valves in the fuel distributor far enough to let in the correct amount of fuel against the too-high control pressure.

A leaking cold start injector is more likely to cause starting problems due to fuel bleeding out of the system with the engine off.

My advice is to beg, borrow, or buy the gauge then report back with your findings.

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Erich Loepke
2010 Ford Focus
Currently Benz-less