I tested the latest version of UBB (7.6.0) on PHP7 (7.0.6) since I just bought a new license this week and my hosting company gives the option to switch between 5.6 and 7.0 on the go (they also removed versions that go EOL soon such as 5.3 and 5.4). They actually encourage their customers to try 7.0 and if possible, adapt scripts for the future that eventually comes. My own custom CMS merely needed to have some mysql connections adapted to mysqli since PHP7 fully removed the original mysql extension.

The UBB Install script couldn't connect to the database, probably due to similar reasons? I had errors off when I tried, so there weren't any details other than the parsing coming to a halt as soon as the script tried to make a database connection.

After installing succesfully on PHP 5.6, I switched back to 7.0 to see if the installed UBB works. No page loaded with ubbthreads.php, and all (like the forum list, portal, etc) returned errors such as these:

Code
Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP;
Smarty has a deprecated constructor in /sites/www/forums/libs/smarty/Smarty.class.php on line 64
Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP;
bbcode has a deprecated constructor in /sites/www/forums/libs/bbcode.inc.php on line 4
Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP;
mailer has a deprecated constructor in /sites/www/forums/libs/mailer.inc.php on line 6
Fatal error: Uncaught Error: Call to undefined function mysql_connect() in /sites/www/forums/libs/mysql.inc.php:20
Stack trace: #0 /sites/www/forums/libs/ubbthreads.inc.php(88): sql->connect() #1 /sites/www/forums/ubbthreads.php(40): require_once('/sites/...') #2 {main} thrown in /sites/www/forums/libs/mysql.inc.php on line 20

Seems like UBB has several incompatible contructors and database calls. I will likely run PHP 5.6 for years and so will most others, but I like how PHP finally gives in and makes things more strict to actually prevent incompatibility issues in the future. It's kind of similar as to how strict XML originally tried to remedy the 'wild' markup of HTML that was all over the place on different software.