Not necessarily. In 2004, Germany introduced a 25 cent deposit on single-use plastic bottles [1] for types of beverages where single-use bottles were much more common than reusable bottles. The intention was like you describe: to encourage consumers and manufacturers to prefer reusable bottles. However, the opposite happened.

In the first few months after the law came into power, each retailer would only take back bottles purchased at their own stores, leading to a public outcry. Retailers eventually came together to form a single deposit system for single-use bottles. Bottles purchased from any of the participating retailers could now be returned to any other participating retailer.

That's something that's pretty much impossible for reusable bottles: When you return a reusable bottle, the store that takes it back must have a supply chain to ship the bottle back to the corresponding beverage factory. Single-use bottles, on the other hand, are just destroyed and recycled, so the supply chain is much easier.

In the end, the deposit system for single-use bottles functioned so well (both for customers and retailers) that manufacturers switched from reusable to single-use bottles. For example, Coca-Cola used to produce only reusable bottles (and single-use aluminum cans). Now they sell a large amount of single-use bottles. A lot of retailers (e.g. the almighty discount chains) sell only single-use bottles because they don't want to bother with collecting reusable bottles.

[1] For comparison: Deposits on reusable bottles are either 8 cents (glass, e.g. beer) or 15 cents (plastic, e.g. juices; sometimes glass, e.g. brand sodas).