Is it possible to boot with a completely blank hard drive, from a USB stick?

I have a Lenovo Yoga 3 Pro, and am ordering an upgrade for the hard drive. If I put a linux OS on a USB, and physically swap out the two hard drives, will I be able to turn on my computer and have it boot from the USB drive?
I know only a little about BIOS/UEFI. Is this stored somewhere else than the hard drive? Will I have to adjust the boot order prior to doing the physical swap?

Yes, you can make a bootable USB flash drive with an OS on it.
Yes, you have to adjust boot drive order in BIOS. That information is stored on a chip on the motherboard. The coin battery keeps that alive to be called up when you need it changed or when the computer is started.

Bios is stored on the motherboard.
It then enters the registry and drivers stored on the hard drive/ssd, then it goes to Windows, and if successful, ta-da.

If you put Linux on a thumb flash drive, you are still missing drivers and I'm not familiar enough with how Linux operates versus Windows with its registry.
The bios boots to a point before DOS would run if I remember correctly.

As I answered before, order an M.2 enclosure and just clone the drive that is in there now and swap them.
That is the normal way. I do not believe the bios has any instruction to boot in Linux, but there are very few experts on the subject. I know what every part of a computer is and how they interact.

The BIOS is separate from the hard drive. Many will have the option (which, yes, you'll probably want to do prior) to boot from USB or removable media.

I'm not sure what you are doing with your hard drives. I think you are removing and putting two new ones in.
As you seem not to be putting a system on them they will not have the boot sector setup so Bios will just drop through to find a genuine boot sector.
USB can be different being seen by bios at that stage. So best to Depress F12 at swich on so you can inform bios to use the USB. As long as it has a good boot sector which will have been created by the Linux setup.
Bios does not access registry or drivers as suggested. The last thing Bios does is to access the boot sector in sector 0 and enters that code which carries on and eventually loads up windows