I think it's too early to say if there's an impact on litter yet. It's only been a few months. I do volunteer litter picking in my area and plastic bottles are part of the waste but mostly it's other stuff, so I don't think it will make a big difference.
We have kerbside pickup so now it's just made it either more expensive or more hassle... I hate it. People who were already recycling will be the ones who bother to keep another bin for just these returnables and then go to the shop to put each one in the machine individually, then get a receipt, then go to the shop to redeem it for money. It's a huge hassle and the machines are a waste of energy and ugly.
In Germany we've had this all my waking life. I personally don't find it a hassle at all. The bottles don't go bad when they await my next trip to the shops. It is so natural for me to return them and get my depos back.
Whenever I'm out of the country I feel so bad about throwing bottles into the rubbish. They must return to their natural habitat!
The thing is, we have kerbside pickup so the bottles weren't going in the trash before. It's just that now I have a lot of extra steps and need to keep yet another separate container for plastic.