Cook a thawed turkey

It is possible to over brine meat. If you leave it in too long it will get too salty.

If you use a more dilute brine it won't get as salty but you will wash out more of the natural flavor into the water as well.

You could submerge your turkey in its packaging in ice water in a cooler for a day before brining. You could even thaw the turkey in this manner if you made sure to keep it in ice water so it didn't get to 40F.

I have been in this situation before and I did try freezing it. When I used it later on, it did taste and feel OK, but as you would expect, not the real fresh taste.

I do not think the ingredients in the marinade will have any effect while it is frozen. While thawing, the yogurt might split, leaving more than usual water, but that shouldnt alter much of the outcome. It will be still good after defrosting; I would normally defrost by leaving the item in the refrigerator overnight, rather than quick methods like microwaving or even leaving at room temperature on the kitchen counter.