I have the Klepper rig on my my kayak and the short answer is yes, you can lower and raise both sails while underway.  

 The long answer is; while you can raise and lower the sails, if you use the rig as-is from the factory you would have to stand up in the cockpit in order to lower the main and devise some way of keeping the jib from going in the drink.  I slightly modified my rig so that I can raise and lower both sails without even having to pop my spray skirt.  I would like to put a small roller furler on my jib, but the system I have in place works fine for now.  Feel free to email me if you want any extra details on my modifications.  

Probably should have put my email in there, it is casey at keakayaks.com  (no spaces and replace the at with @)