Would it make a difference to clean the data before using R findCorrelation()?
In most cases, you will want to run findCorrelation after cleaning. The reason being the cleaning process is either removing unwanted data points (that you deem irrelevant anyway) or computing some transformation that you'll want findCorrelation to be aware of. 

Now, that said, I've often run it twice, once before cleaning and once after if my transformation could alter the correlation structure of the data.

Fortunately, since you're using caret, it is a simple matter to estimate your models both ways, then compare the ultimate differences in accuracy.  Unfortunately, the correct answer to many questions in ML is 'do it both ways then compare'