why a 20?
If you want a turkey gun, I'd get one that's chambered for a turkey shell, meaning 3" 12 ga. (for me, the 3.5's are overkill, and 10's too darn heavy, and turkey hunting IS walking) and all the turkey gun bells and whistles.
(X-F choke, cammo, etc)
Sure, you can hunt (and kill) turkeys w/ a 20, its been done plenty I'd guess, and the new space metal loads and spec chokes add some clout, but the same applies to the 12, so your shorting yourself of 15 yds or more of range I'd think. Course, maybe you want to hunt w/ that handicap. Some guys bowhunt turkeys.
When I hunted turkeys as a teen, w/ my hand-me-down 12ga pump (2.75 chamber, Savage model of 1921, full choke) I used , 1-1/4 oz of #6 shot ( it was recommended to me NOT to use short mags in the old girl) I figured my effective range was 30 yds., and 25 or less ideally. I'd say the same applies to a 20, even w/ tung shot. (3" 20 ='s 1-1/4 oz of shot, yes?)
Finally, in a fit of nostaglia, wanting to bust a turkey w/ her one more time like the old days, I dusted off the old Savage and patterned her again w/ 1-1/4 oz of #6 lead recently. I then compared those patterns to my real turkey gun using 3" 1-3/4 of #5 lead, which is a preferred load in it. I was putting twice, say again, twice, the amount of shot on a 9" pie plate at 30 long paces as I was w/ the vintage Savage. There really was no comparison.
All that translates into more killing power/cleaner kills. With the variables of uncentered patterns due to whatever, patterns spoiled by intervening brush, and misjudges in range, the 20 starts to look real iffy in my book. So does the 2.75-12, 1-1/4, lead and std full choke for that matter.
The turkey is such a grand bird, and so difficult to get on and in range (most times anyhow) that I want to use plenty of gun. And I do not want to get in a foot race w/ a cripple or have one glide off never to be found.