I think, Yii will work fine with (relatively) large amount of data. I'm using Yii to manage 1.3 million records, some thausend updates a day and some thousand querys a day on an small virtual host with an amazing performance.
If your database can handle this data, your Yii application will also handle that.
Your choice of the database will be an important point. So @Denis said some important thinks. By using MySQL probably you have to explore / determined the right storage-engine for your needs.
But, there are some points, which i realized by creating an growing project with Yii. You should think about those things:
-Yii is an young framework: new technologies (like ajax) are supported, but in some special cases it's a bit immature: it's very easy to generate an basic application in a cuple of hours. Problem could be occur by special situation and requirements.
Example: they have an nice validation-mechanism for user inputs(HTML Forms). But until Yii 1.1.6 that doesn't work with HTML Checkboxes, since Yii 1.1.7, Checkboxes are supported by default, but no groups of checkboxes. An other problem: Yii alway uses an table alias, which is always "t". That could be a problem! Sometimes you can define that alias, sometimes not (which is inconsistent). If you like to lock a couple of tables in MySql, you ran into a problem, because Yii calls every table with the same alias "t". So you are unable to loot the tables in MySql by tablename and it's also impossible to lock a couple of tables, which called by the same alias. -> those are specific problems, you can solve them, by writing pure PHP (not using Yii functionality) What I'm trying to say: the framework will not be helpful in very case, but in mostly.
-Yii is easy to extend. It's easy to add own extensions or functionality. So lot's of those "small problems" can be solved be writing own extensions, widgets or by overriding methods.
-Yii supports PHP 5.2. Yii is compatible with 5.3 but (Yii runs on 5.3 - i'm still using it since yesterday, it work's) but doesn't support new features from 5.3 (maybe you need one?)
PHP5.3 will be (maybe) supported with Yii 2.0 - in a distance future (2012)
-Yii has a small (but very good) community.
-there is no professional support (you can post bugs in hope, anybody will fix it - or you will fix it yourself)
-Yii is OO PHP. Think about that by handling with Data-Objects. It's possible to load large amount of data into Data-objects. But keep in mind, that your application server have enough RAM (but that's not a Yii specific thing)
At all: i like Yii an if your application is not to complex, you will have a lot of fun an an nice and powerful application at the end.