Yes it will, and *ideally* the next step is to use the clone tool to clone your current uSD Image to a SSD, shutdown, remove the uSD and reboot from the SSD and be in business to continue as normal.
The truth is that it may not happen so smoothly as that.
Probably if you have chosen a HDD or an external SSD like a Toshiba T5 or SanDisk Extreme Portable SSD it will work and will continue operating normally with very good performance. HDD somewhat slower for obvious reasons. Trim will not work but hey these drives never intended to need trim.
If you chose a SATAIII style internal SSD and an off the shelf USB3 adapter cable - you would have probably first noticed when cloning the uSD to the drive the write speed was kinda poor. The first sign you have issues. Try booting from the fresh new SSD and deep disappointment when nothing seems to happen.
You are smart and attentive and realise there is a fix - add a bit of code to the beginning of the /boot/cmdline.txt file: ‘USB-storage.quirks=xxxx:yyyy:u ‘ where xxxx and yyyy correspond to your particular interface cable. Now you can boot at USB3.0 speeds and pretty much good to go.
You learn then about trim and UAS - the two reasons you probably chose a real SSD but didn’t know it. To get this working correctly you need the ‘good’ interface - Eluteng is the brand you need to find, Amazon seems to be the best source. (Still waiting for mine!)
Now, that green LED is constantly winking at you and the Dmesg ring buffer fills every few seconds with errors. The fix for that is a blank formatted uSD card in the PI 4’s. card slot. Easy fix provided you have a uSD card laying around.
I can’t fault the RPI effort - the nonsense seems to be with the Linux kernel.