It depends what the updates are for
I would say they're probably not important, you can update Windows automatically and if you need driver updates you can get them from the manufacturer's website, same with other software
Someone else correct me if I'm wrong though
EDIT: Quote from site - "Updates from HP or Compaq Connections is a messaging service that comes pre-installed on HP and Compaq desktop computers. The service provides product notices, support updates, tips, and special offers specifically for your model of HP or Compaq PC."
It doesn't seem necessary to me, again correct me if I'm wrong please
If there's something really important, they'll post it on the website, you don't need that running all the time just to tell you the odd thing