In general, anything is possible.
As you have access to the source code you can do a lot of stuff with Limesurvey.
But from my point of view, you will have to do a lot of customization to get to what you want to do.
And measuring reaction times over a web application is quite questionable anyway, because there can be so many other factors that influence the measured time (delay, slow internet, etc.).
I assume that the times that you want to measure will range in the second or rather milisecond range and I think the internet connection can have a strong impact on this.