C3S

hendyalheety,

Of course it makes sense to deduct free CaO before evaluating c3s.
However, in the end, it depends on the purpose of this evaluation.

If you want to predict the actual c3s content as it would be measured by XRD, then accounting for free lime would likely improve the correlation with measurements. However, it is well known that the Bogue formulas do not correlate so well with measurements. This is because the underlying Bogue assumption are not valid in reality. For example the c3s phase would allow inclusion from other species, like alkalies. Lime can also combine with other species. Many people have used more detailed models to predict actual phase compositions more accurately. Sometimes the principle is the same as the Bogue exercice: assuming the potential phases compatible with the phase rule. Sometimes it is more sophisticated by modeling the solubility of secondary species in the main solid phases.

However, the initial purpose of Bogue was more to evaluate the "potential phase composition". In this case, by purpose, the free lime should not be taken into account. Indeed, the hypothetical free lime could potentially by turned into c3s by combining with c2s. Deducting free lime would then define a "potential phase composition assuming a certain amount of uncombined CaO".

It all depends on your purpose, and maybe on some conventions.

You can find a lot of litterature abou this.
This paper: 

http://www.hindawi.com/journals/ijac/2010/102146/

discuss the fate of c3a as a function of the SO3 content.
It mentions that Al2O3 can migrate to silicate phases when SO3 increases.
This gives an idea of the real physics that goes on.