Broadly speaking, yes - moving your router from 20MHz to 40MHz will increase your wireless speed. However, there are a few things to keep in mind.
First, not all devices support the higher 40MHz bandwidth. So you may see a decrease in speed if you have older devices that can only connect at 20MHz.
Second, the increased speed comes with increased interference. So if you live in a densely populated area with lots of other wireless networks around, you may actually see a decrease in performance due to interference.
Third, the extra speed is only really useful if you're doing data-intensive tasks like streaming video or gaming. For most general web browsing and emailing, the difference between 20MHz and 40MHz won't be noticeable.
So overall, moving to 40MHz will give you a boost in speed - but it's not always worth it, especially if you have older devices or live in a crowded area.