Generally no — adding a proxy adds an extra hop between you and the destination, which usually makes things slightly slower, not faster.
The caching exception
Some proxies cache frequently requested content, so if many people behind the same proxy request the same page, subsequent loads can be faster because the proxy already has a copy. This applies to organizational and ISP-level transparent proxies more than personal ones.
Why free proxies are usually slower
A free public proxy is shared by everyone using that list at once, and the server itself often has modest bandwidth. Routing through it adds latency and can bottleneck your connection well below your normal speed.
The honest takeaway
If speed is your actual goal, a proxy isn't the tool for that. Use one when you need a different apparent location or IP, not because you're expecting a speed boost.