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: 
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!
If you select the option "erase entire disk" option your entire disk partition scheme will be erased and the entire disk space will be alloted to Ubuntu.

To prevent this you can try using "advanced partitioning tool" during formatting.