I'm trying to download a website that offers paid subscription type of
membership for access to their database.

The site allows you to make a temporary account to gain full access to their
site.

Is it legal to download such site for my personal use?  I'm not copying the
content to sell or anything.

Here is the disclaimer from the website:

Ownership and Copyright Notice

The information and content made available on or through this Site is the
property of, and owned by, xxxxxxx(excluding content provided by others), and
is protected by copyright and other applicable laws. xxxxxxxx reserves all
rights therein. Information received through this Site may be displayed and
printed for your personal, non-commercial use only, provided that all
copyright and other notices contained therein are left intact. You agree not
to modify, reproduce, transmit, distribute, copy, license, disseminate, sell,
publish, create derivative works from, publicly display, publicly perform,
edit, translate, reformat, broadcast, or circulate any information obtained
from or received through this Site to anyone, without the express prior
written consent of xxxxxxxxx.