Hi,
I have a computationally costly FE model with 8 inputs (with a dependence structure) and multiple outputs. I am using PCE to build a metamodel for analyzing the forward propagation of uncertainties.

Right now I am using the built-in ANCOVA method to perform the sensitivity analysis and it works well.

I also want to calculate the Kucherenko Indices and my idea is to do the following:

Evaluate the model output using the costly model

Build a PCE-Metamodel

Generate a large number of samples

Use these input-output samples to estimate the Kucherenko indices.

Am I thinking correctly? Is it possible to execute this in UQlab?

Yes, I think this procedure is correct.
I am currently working on a project with a very similar structure. In my problem, I have 20 input variables, and I am struggling to find a good fit for the model, which also has dependent input variables.

If I were you, I would be sure that the computed PCE is accurate enough with the computational results. You can do this by either analyzing the LOO error (or the modified LOO error), plotting the histogram of the computational results and the PCE prediction, or even collecting a test dataset from your initial experimental design and testing the PCE prediction.