Not a tremendous amount, about a volume's worth. But to do that, you'd have to have the equipment to pressurize/purge, and then do it, what, 25x? I don't have such equipment, unless one considers tightening and releasing a TC clamp 25x a job to which one can look forward.
There's another issue I haven't mentioned, primarily because I know it may cause a couple heads to explode. That is, bottled CO2 isn't pure, unless you've taken pains to purchase that. Beverage CO2 probably is 99.5% pure. The rest? Air and such. Air is 21% oxygen, so even with bottled CO2, you're not getting a perfect purge.
Perfect? Not in purging a keg (pushing Star-San, say), and not in purging hops. How much does it matter? You decide. As for me, I'm always moving toward perfection, if I can. It's simply a personal philosophy--do the best I can. Using fermentation CO2 is pure, and I'd rather use that than bottled CO2, if I can.
It's why a lot of LODO brewers do spunding of their beer, which is to move the fermenting beer, with about 5 points of gravity remaining, into a keg to finish. Seal up the keg, and voila! Carbonated beer without using bottled CO2 which isn't perfectly pure.
I'm doing a variation of that, sealing my fermenter and carbonating it partially in the same way. Problem is, I have to complete the carbonation using bottled CO2, which is impure. But there's less O2 going into my beer that way than if I'd just carbonated using bottled CO2, about 2/3 less.
I've seen the results of this care in the length of time my beer stays good while on tap. Months. So I keep plugging away, trying to eliminate O2 as much as possible. Seems to work.
There are many in this thread trying to puzzle this out. Whether it's worth it depends on one's motivation, sensitivity to oxidation, time to empty before oxidation has serious consequences to flavor, resources, time, and so on. If it cost me $5000 to get the last bit of O2 out, I wouldn't do it. But if it costs me $50 to try, well, I will.