MacBook – Does the MacBook Pro 15” 8,2 Early 2011 accept both A1321 and A1382 batteries

Much like the commercial versions you mentioned, what you want to do is possible (that there are commercial versions essentially proved this).

You'll need to chop apart a MagSafe cable or figure out how to interact with Apple's airplane adapter. You'll also need to figure out how to interact with the batteries to get the correct voltage (and maybe do cell wear levelling).

Also, I doubt the MacBook Pro batteries will last anywhere near as long or be as reliable as the commercial versions.

(There was an original answer, but it made incorrect assumptions that were addressed in the comments. See the edit stack for the originals.)

Batteries are the one thing in a laptop you shouldn't mess with -- I'm fairly sure they're the only component in your computer that is in a constantly controlled risk of overheating, catching fire or quite literally exploding. When they are not made to the utmost standards of quality, you could be, again quite literally, putting your life at risk. I'm not saying this is the case with you, and fortunately not with me, but if I were unable to afford a new manufacturer-supplied battery to replace a dying one in my laptop, I would rather sell it and buy a cheaper laptop whose battery I could afford.

I agree Apple's markup on batteries -- and quite generally most of the accessories they sell -- is excessive, but batteries and chargers (due to the risk of electric shock) are two things I would never buy from anyone but Apple. If you search around you will find teardowns of original Apple chargers and cheap Chinese knockoffs, and even if you have zero knowledge of electronics, you can tell the Apple chargers are much higher quality than the Chinese knockoffs. This is quite hard to tell with batteries, but do you believe for a moment the lowest bidder won't cut costs exactly as they do with chargers?

And just to stay on topic, yes the battery is quite important. 7.3 V sounds like a two cell Li-ion configuration while 10.95 V would be a three cell Li-ion battery. Using a two-cell battery in place of a three-cell battery or vice-versa is a sure-fire recipe for disaster -- even if the electronics could take the different voltage, over-charging a two cell battery with enough voltage for a three cell battery would immediately damage it. In case of a high quality battery, only the protection circuit would be damaged, but in case of a low-quality knockoff with no protection circuits, the battery would be immediately and irreversibly damaged, with a symptom of either swelling, fire or an explosion.