I don't know if there are any additional issues that arise with using goodness off fit with a piece-wise function. When I have fit generalized pareto distributions to series like financial market returns, I have noticed that it is common to differences between the estimated distribution and observed returns at the cutoff points. This is going to be the main difference between running the goodness of fit test on the entire GPD as opposed to the fits for the tails individually, since the kernel density fit will be good.
If you have an estimate of your hypothesized distribution, I would recommend using the Anderson-Darling test instead of the KS-test. The KS-test checks for the maximum distance between the empirical distribution function and the hypothesized function, and thus is not that sensitive to the tails which is what you care about. The Anderson-Darling test integrates over the squared difference between empirical distribution and the hypothesized, and places different weights on each part of the distribution. The weighting function effectively places greater weight in the tails.