The number of apps installed isn't important. Or at least not directly. However, if you start to run out of storage it can affect overall performance. The iPad is constantly reading, writing, and erasing parts of storage. Less storage can make this process less efficient.
Imagine you own a big warehouse full of shelves. As long as there are lots of empty shelves, adding stuff, moving stuff, and shipping it out is fairly straight forward; but if your warehouse is getting full you may find yourself having to move stuff to make room, or clean out old unused boxes before you can do anything else. It adds a lot of overhead to the job. It's not exactly the same, but it's a similar situation when the iPad's storage gets limited.
It's a good idea to leave 3 to 5 GB of storage free on your iPad. Or so I've heard recommended. This is one of the reasons I'm so pushy about recommending people not get the 16GB models. You only get about 11 GB of storage after the OS and native apps are installed. That's not a lot of room to grow.