Yes, you can, but you would have to configure web server per your needs.
If you set up Block Storage using on-creation instructions, you will have files in /mnt/volume-name. To make it accessible by URLs, you would need to add appropriate server block.
Something like explained in the How To Move an Apache Web Root to a New Location on Ubuntu 16.04, but you would add new block instead of editing existing.

If you give us more context, e.g. where your volume is mounted, what web server you are using, etc.. we would be able to give you more specific instructions.

Thanks. So, because it is like an external hard drive – with no operating system of its own – one would have to have another droplet with LAMP (or similar) set up. I think that answers my question. Much appreciated.