There are two ways to look at this question. On the one hand, in the literal sense, your arms are going to get tired after a while, yes. But, the joy of kayaking is you can take a break from paddling and coast around for a while (depending on the narrowness of the water).
Now, regarding whether or not this activity gets boring after a while, that is simply a judgment call. It also depends on where you are kayaking as though lakes and oceans are more wide open; rivers tend to offer better sights and overall adventure.