You can hunt turkey with #4,5, or 6 shot with a tactical short barrel shotgun IF the barrel is threaded & will screw in atleast a modified or full choke. With a open choke, you will be lucky to hit a turkey with a couple pellets, and unless one finds its way to the head, then the turkey will just take off wounded and never be found. Open chokes are fine for shooting rifled slugs at medium to big game animals though, but limited range without practise & familiarity of the firearm. If the tactical shotgun is a popular brand like a remington 870 or mossberg 500 series, then used barrels in other lengths are common, and cheap used, and will have a screw in type choke that you can get a full or xtra full choke for turkey, and then you can drop a turkey at 40-50 yards with a well placed head shot....a turkeys body is thich & tough, so body shots just wound & destroy the meat.
With that being said, if shtf & you were trying to survive, and no law or government existed, then you would not have to follow strict hunting laws that are in place. With no hunting laws, a turkey could easily be killed with one single shot with a .22lr to the head or vitals..again, only consider this option if shtf & it was a matter of life & death...never do this now, or you will have serious legal issues...only suggesting this if shtf & no mnr, law, or government was in place, and the world is in chaos....If shtf, and with practise a .22lr would be my primary source of food, and I own over a dozen guns, crossbow, & bows...I have a deadly accurate Ruger SR-22 with a bipod, leupold scope, and trigger job, making it very accurate, quiet vs a shotgun and easy to carry 1000s of rounds of various types of ammo with me at all times...I could shoot subsonics very quiet, and if a group of hostile people dangers my life, I slam in a 25 round magazine of high velocity CCI stingers and put a end to a threat that wanted to take my stuff & life. Because I practise alot, I can shoot a 2-3" group consistently at 100 yards with my particular .22lr with good ammunition....If shtf, I would likely even hunt deer with my .22 because if a deer was 50-100 yards away, I could drop it with a high velocity well placed head shot...Sure I could drop it with my 308 at 200+ yards, but anyone within 5 miles will know roughly my location...With a .22lr, 1 mile is about the distance your shot is heard, at the most...and then its still hard to pinpoint because it will be a faint crack, and if your in thick forest, a .22lr probably would not be heard from outside the forest...The quieter the better, because after you shoot a deer, you still need to get it out & home, which leaves you vulnerable as your dragging it.
IMHO.....buy a Remington 870.......avoid the Stoeger - not that Stoeger make bad guns, but because the Remington 870 is better quality. Not that being said I hunt with a Beretta 391 and a Benelli Super Nova steady grip.....why you may ask. I feel these are some of the best shotguns on the market - not cheap, not lots of aftermarket accessories but the best quality IMHO - yes better than the Remingtons.
Now I do have a nice Remington 870 Wingmaster tactical zombie gun for when SHTF but for quality my Beretta and Benelli win hands down.
PS
Turkey season is in the spring and the fall - if you do not have a turkey now your outta luck until April 25th. For turkey you NEED screw in chokes - length of bbl is irrelevant but a good quality aftermarket choke is KEY (just choose your the best shell for that choke by patterning your gun). I use a Benelli SuperNova steady grip with an Indian Creek choke (3" #6 2oz loads). Tactical guns are not designed for hunting so why bother