haha, no, with or without ocing it, you will fry it. Thermal paste is what allows the cpu to be in contact with the heatsink. Without it there is no heat transfering from cpu to heatsink, which means a hot cpu!
if you purchase the consumer version of a CPU, it will come with heat sink. the heat sink will have a layer of thermal paste on it so no need to purchase any (unless you want to). also if you purchase an after market cooler, most will come with paste.
if you purchase an OEM version of a CPU (does not come with a cooler) or you simply plan to re-use your old heat sink. then you would need thermal paste.
i strongly suggest using thermal paste, can a CPU work without it? yes, but it can also be severely damaged without it. why risk it?
Make sure you remove all of the old thermal interface material from the heatsink before you apply any new thermal interface material. Follow the thermal interface material manufacturer's application instructions to ensure you get the most effective thermal contact.