Will an external HDD encrypted with 17.10 be accessible with 18.04 after an upgrade?

You should have no trouble mounting the external drive as long as you have cryptsetup:

sudo apt install cryptsetup

Once this is installed you will be able to mount the drive via file browser.

You are using LUKS so Ubuntu is using cryptsetup behind the scene. Normally, encrypted volumne with LUKS should still work after an upgrade unless the default encryption method has changed.

There was a time many years ago, the default aes-cbc-plain was changed and that causes some drives not to mount unless the old encryption method is specifed explicitly. There is no such change between 17.10 and 18.04, so your situation should be okay.

NB: In Ubuntu 18.04, cryptsetup should came installed by default but if you wish to use cryptsetup as a command line tool in bash, you should install cryptsetup-bin

sudo apt-get install cryptsetup-bin