I think the stuff in there might just fall out, depending on the design of your freezer.
Might also cause an issue with freezing, but only if you put a lot of unfrozen stuff in at the same time, whatever is in the middle might take days(?) to freeze. But probably not if you're just putting already frozen food from the shop in there.
You can get new drawers, but they're quite expensive, google freezer drawer spares for a few suppliers.
We too have one freezer drawer that is falling apart and another which did have a pull down flappy thing until a ham fisted friend broke the hinges because he thought it was a drawer and pulled it too hard.
If I'd have known how long that fridge freezer was going to last, I'd have paid the seven quid or whatever it was for new hinges, but it seemed like such a lot of money at the time for a couple of tiny bits of plastic.
So instead we've put up with a freezer shelf that pops off it's mounts as soon as you look at it for over 20 years because the hinges and flap that hold it in place are missing.
Part of me thinks sod it, just buy a new fridge freezer, but it still works so if it ain't completely broke, don't fix it and I'm also quite curious as to how long it is going to last.