photos on external hard drive

One more thing - there is no problem with additional Photo Libraries on an external drive.

But when you move the library used for iCloud to an external volume, you are moving the System Photos Library.

Then you have to ensure, that the external drive is always mounted, as soon as you log into your user account. The background processes need the System Photos Library to be available, even if you are not working with the Photos.app. Keep the external drive connected at all times, so you will not forget to mount it immediately after logging into your user account.

And do not forget to include the external volume with your Photos Library into your regular backups.

If you mean will they still sync to other devices via iCloud Photos, yes they can if you designate the library on the external drive as your system photo library. See the information in the following:

Move your Photos library to save space on your Mac - Apple Support

and

Designate a System Photo Library in Photos - Apple Support