Just the opposite!
 

I bought a Savage 16 youth model for my grandson about 6 years ago. He has since grown substantially and is approaching the 6' mark. There was a post on here about shortening a synthetic stock but I'd like to know if there is a way to lengthen one.
I do have a rubber slip on that will add another inch or so but I'm trying to figure out a way to make it more permanent and still look good. Any suggestions?

if I was you, and if possible, as I am just not sure
maybe look and see if they sell full-sized stocks for it, and maybe sell the youth stock, many savage rifles all use the same stock, so, you might find someone wanting a youth stock that may even swap you
I also know they sell spacers for the recoil pad,(way more common with shotguns, but sure you can fit them to this rifle) that I imagine you can add to get as long as you want, but if it was me, I'd suck it up and just get a solid stock of correct size, than have one pieced together

How much more length are you needing? I’d get a slab of marine board and shape it to fit, key the shims together with pin stock, and use longer mounting screws for the factory buttpad. Done in a couple of hours, including cleanup.

also keep in m ind, that if this is a TRUE youth stock, the distance from grip to trigger will be shorter too, and that your not going to fix by adding a longer LOP to it!

That may be a good idea looking for someone to swap out stocks. I didn't think of that.
I'm pretty sure that is all incorporated into the different stocks. The action will fit either youth or adult stock. But yes a true youth stock has a shorter LOP and grip to trigger length for smaller hands.

See what happens in the classifieds. I have to see what it looks like under the recoil pad. I just might go with the marine board.

might b worth placing a add on some other forums too, like maybe the PA firearm forum, , this time of year a lot of shooting/hunting forums get busy!, helping maybe find you a willing swap or?? in PA

maybe a laminate from stockysstocks.com