The extender will add some resistance due to the added pin contacts, but I don't know if that will effect anything, probably not very noticable, but you should compare your final tube selections without the enxtender if you plan to not use it later. It's more important to make sure all the pins are clean and tight, that's bigger source of pin contact resistance.
But the extender would make it easier to get a grip on the tube when removing it. The stock socket positions the installed tube a bit low inside the case making tube removal difficult, iirc.
I wouldn't worry about wearing out the socket. You can always tighten it up by bending the contacts closer. It is probably the same 9 pin socket used in the Minimax preamp which is famous for prodigious tube rolling, and nobody ever mentioned a socket getting loose. Even when using the extender, you still don't know if just the tube or the tube and extender will pull out. Maybe removing the DAC cover will make removing the tubes easier during the rolling. Power off when swapping, of course.
Do the opamp rolling before you do the tube, because the opamps are always in the circuit, even when the tube is engaged, and the opamps will have a big effect on SQ. The stock opamps are LM4562, my least favorite for music - stuffy.
Incidentally, my favorite 12AU7 tube is the stock EE tube that comes with their 9 pin products. It is not lush or warm, but very accurate and clean without thinning or harshness and it has decent bass. Excellent tube for $10. Of course there are better, but if you like clean tube sound, add it to the mix of your comparisons.
I personally would not spend a lot of money for a NOS Mullard or something exotic like that when there is an opamp coming after it. Any opamp compatible with the EE DAC will have 100dB of negative feedback built in. Some do it better than others, but you'll never hear the tube as you would in a no feedback, all tube design. There are some good threads here and AC about what opamps sound best in this DAC.
When I auditioned the DAC I preferred no tube setting. But iirc that was the version 1 of the DAC, with stock opamps, and I don't know what tube was in it. Other people preferred the tube switched in.
12AT7 will give you more gain than 12AU7, so make sure your preamp VC is not too low when playing a loud signal like a pop tune.