As far as I am aware, it reports back with statistics on how the product is used to help HP develop and improve their products so I imagine it could well report any errors that your printer encounters. It is not responsible for updates - you should have a seperately installed application called HP Update which is resposible for this.
Obviously, every system is different, but I can say that I've uninstalled it with no loss of functionality - I also remember receiving a similar warning when uninstalling.
Just as a point of interest, during the initial stages of installing the printer software suite, if you choose the Advanced Options, you can select not to install this application ( and other optional components such as Photosmart Essentials, Shop for Supplies etc ).
On the link below is a thread on another forum regarding this that you may wish to read.
Hope this helps.