Welcome in the forum and in the fascinating world of PSoCs!
Short answer: Yes, you can.
Long version: The Filter component has got 128 bytes of ram area to store filter coefficients which you may change under program control.
Very long version: The filter block is a programmable DSP. There is an assembler you may use to construct your own algorithms for filtering.
But; I can assure you that this is nothing for the newbies, it is complicated as .... (language barrier involved).
I would suggest you to:
Download and install (complete) PSoC Creator. This will give you access to all the documentation and a heap of example projects.
Installing the Kit-Only files for your evaluation board. So you will get some board-specific examples additionally.
Programming will be done in C-language, so get hands on a manual like this one.
Nathan, I suggest doing a Google (or other) search for The Filter Wizard who is Kendall Castor-Perry. He has a blog on Cypress for all things about filters -- FIR, IIR, time aligning multiplexed inputs. You will find a fantastic filter education with him. The short answer to your question is YES you can do the cutoff in real time -- even with multiple input channels at audio frequencies. You can also do a search for The Filter Wizard in this Cypress Community window.