Technically you could if you can keep temps low enough, but odds are before you can get into the bios and downclock everything you'll overheat and crash. I'm also not sure if you'd even be able to downclock far enough to make the computer usable. You really should just wait for the thermal paste.
The CPU will come with a heatsink and there will be a little "pad" on the bottom. That's thermal paste. Since you ordered thermal paste already, just wait for it to come and don't install the heatsink because it will apply the paste as soon as you lock it in.
Take some rubbing alcohol and take off the stock heatsink paste and then when your new paste comes just reapply it on the CPU like normal paste and use the stock cooler. It will actually help you out a little.