Question: I'm considering ditching Windows 8 and doing a fully clean install of Ubuntu. However, I'm concerned because my computer came with a built-in 16 GB recovery partition that would need to be erased as well. 

If I pick the "erase entire disk" option during installation, will it wipe out this recovery partition too?

Answer: 
Using the "Erase entire disk", will erase all partitions.

Since you're new, I would recommend to start with dual booting with Windows first. Get used to Ubuntu and then you may decide later to remove Windows completely. This is especially recommended if you do not have recovery media or another means of reinstalling Windows should you wish to.

In any case, I would recommend doing a backup of your important data on an external disk before trying to install Ubuntu. If something goes wrong, your data would be safe.
Yes, it will.

I've switched from windows 8 to Ubuntu a lot. It will destroy your recovery partition, but it is worth it. SO WORTH IT! You should totally go through with your Ubuntu installation. You will be happy with what you get from it!