In general that certainly is possible. Actually every QRCode / barcode stores information. But usually the size of that information is pretty small. Typically only references like URLs or numbers (IDs) are stored and the 'real' data is retrieved from a database using those references. But strictly speaking that is a form of storing information in a QRCode / barcode.
Looking closely we see that the data is stored in the code itself, not inside a database if we are talking about that small amount of data. Certainly that data can be stored inside a database when the code is read, all you need is a trivial piece of software. But that makes little sense in most cases, since the data already is stored. If you want to use a database to combine data from different sources, so if you only want to use codes as a means of transport, then reading the codes is just a replacement for typing the information in with a keyboard. So no magic here, nothing code specific you have to consider.
If you are talking about bigger amounts of data, then you have to use other types of codes. The one I like most are dataglyphs. They even provide a pretty big fault tolerance.