Yes it would, If the spiral arms were say in the process of expanding that would have an effect on the reading of the doppler shift. The problem making measurements with the spiral galaxies is they aren't symetrical and uniform so what is happening on one side isn't necessaraily happening on the other to balance it out. So when you compare the rotating away side with the rotating towards you side without knowing what else is going on the results will be off.
Yes it would, If the spiral arms were say in the process of expanding that would have an effect on the reading of the doppler shift. The problem making measurements with the spiral galaxies is they aren't symetrical and uniform so what is happening on one side isn't necessaraily happening on the other to balance it out. So when you compare the rotating away side with the rotating towards you side without knowing what else is going on the results will be off.
However, remember that we have access to millions of spirals in the universe through optical observations. Statistically, if a spiral galaxy is behaving in some odd way, we would should see it, unless the timescale of the odd behaviour is extremely short.