...Yes, as-stated, it would affect the stereo image, in your example, relative to without the sidechain (the panning positions won't change). The drum transients would be loudest for the most moments, creating a pumping effect through the mono sidechain, affecting the strings (and obviously the vocals, as they're centered), even though they're (100%?! really?) on the other channel. Therefore, the right channel will have some pumping, and the left will be causing most of it. Without the compressor's internal sidechain, unless you have a poor limiter on the Master track contributing to overcompression, there would be no pumping on either channel.
It would be your sidechain doing it, NOT inherently a compressor with the capability for linking both channels together.
But the real question is, why would you do it that way? It's not practical unless you were specifically emulating a live performance and you just didn't mic the drum kit with more than one mic. Furthermore, couldn't you just sequence a silent kick drum (sending with no volume to the Master) that lines up rhythmically with the original kick drum, and sidechains to the strings to make them duck?
And why not just try writing this yourself and seeing how it works in real life?
Below are some explanations on L/R, stereo, and M/S processing.
For instance, Density MKIII (a free VST plugin you can test) has the option of L/R processing, stereo processing, and M/S processing.
If you link the left and right channels during L/R processing, the knobs associated with L/R move in the same way at the same time as you adjust them. i.e. They are locked to be in "sync".
In contrast, stereo processing in that plugin allows you to affect both channels, but in differing ways if you so desire. You are not constrained to set one knob to X AND set its corresponding knob in the other channel also to X.
And just to be complete, M/S processing allows you to independently impose compression on the middle input (closer to fully mono in the stereo field), and the side input (closer to fully stereo in the stereo field).
A stereo-linked compressor therefore imposes a specific compression processing to both channel inputs in the exact same way, independent of what comes in. What comes out could sound different depending on what is in the stereo field, but that is usually going to happen anyway unless you have identical L/R channels.