Hi @Mouse2721,
Welcome to the HP Forums! I would like to try to answer your questions to the best of my ability. When the printer is connected to the wireless network it has the capability to obtain auto updates. When the printer is turned off it will no longer be on the network thus can not get updates. This does not mean you have to leave it on at all times, it is only a message to make you aware.
AS for the power consumption, I do not know how much electricity is used when the printer is left on, but I can assure you that "This product is designed to reduce power consumption and save natural resources without compromising product performance. It has been designed to reduce total energy consumption both during operation and when the device is not active. This product qualifies for ENERGY STAR®, which is a voluntary program established to encourage the development of energy-efficient office products."
Figure : Energy Star logo

ENERGY STAR is a U.S. registered service mark of the U.S. EPA. As an ENERGY STAR partner, HP has determined that this product meets ENERGY STAR guidelines for energy efficiency.
If you go away for a period of time, it would be best to turn the printer off to help prevent the cartridges from drying out. When you return and the printer is turned back on, it will reconnect to the wireless and obtain any available updates.
To keep cartridges from drying out, always turn the printer off using the Power button, and wait until the Power light goes out before you pull the plug or turn off a power strip. This allows the printer to move the cartridges to a capped position. - SourceAs you can see, this was a very good question, one many others might be wondering about too. If this satisfies your inquiry, please click the Accept as Solution button below so others can find the answer they might be looking for.
Sunshyn2005
I work on behalf of HP
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