So in other words, the application will work just fine the day you sign off assuming the client doesn't update the language core.
Which is no different than with Dreamhost in this scenario. If, for example, PHP 5.X or 6.X ends up breaking your code, it's not like Dreamhost is going to debug it.
There's no functional difference here between PHP and any other language except that the hosting provider will automatically update PHP. And there's no guarantee that won't bork something else (which they will also not support).
No responsible webhost would just roll out a new major version of PHP without warning. Dreamhost have made their servers support it, which means that it is now an option that you can pick, along with PHP 5.2, and 5.3, in multiple modes (cgi, fastcgi, etc.).
But even so, if I build some PHP code that isn't future-proof for even the warranty period that I offer on any code, then I've got to fix it at my cost. If I build some code that, in 3 years time becomes incompatible with a new version of PHP, then it can be fixed then. I can't be expected to predict the future of PHP and build forever-proof code, though.
Which is no different than with Dreamhost in this scenario. If, for example, PHP 5.X or 6.X ends up breaking your code, it's not like Dreamhost is going to debug it.
There's no functional difference here between PHP and any other language except that the hosting provider will automatically update PHP. And there's no guarantee that won't bork something else (which they will also not support).