Unfortunately that is something that is wiser not to assume. As an example there have been updates from HP and Microsoft for devices that have caused havoc for many PC and notebook owners. Do a web search and you will see posts from angry owners.
For wireless adapter updates on HP products it is smarter to stick with the ones that HP provides instead of those available at Windows update. If you owned a Toshiba notebook I would be making the same statement about a Toshiba product.
The method that I suggested and highly recommend about making a custom refresh image is a best practice to follow. If it is too advanced for you to anage, then I sugest using a cloning (disk imaging) product from a company such as Paragon with a free or paid version to accomplish essentially the same result.