no, normally the stock heatsink works for normal use, but at very high temps, if you do a stress test with the stock heatsink you will experience extreme high temperatures, so if you think in overclock it is something more than obligatory, and even if you don't want to overclock, it will help the cpu to stay cool even on very hot days working at 100%;
the thermal paste only need replacement when you take of the cpu, so it is good to change the paste also, but there is no need for replacing the cooler, unless you want something colder, or if it broke by some external factor;