Yes your experiment is possible. If all you need is the cued and uncued times its easy. Users can run an online applet demo provided by psytoolkit. You can embed the applet in a survey where users can record their times. For more in detail data analysis I recommend that you roll your own based on psytoolkits model. Given how simple the experiment is even starting from scratch should be easy for a computer science undergrad with some experience in .net or another web language.