No, it is not necessary. Using HTML5 also does not mean using all the tags it offers. It means using tags and syntax compliant with the HTML5 standard in-progress.
The question of which tags to use is not straight forwards. If you are remaking an existing website, meaning you already have visitors, you should aim for using tags that the majority of your visitors will be able to see correctly. This means digging into stats for browser and versions. When I introduce new features to an exisiting website, I try to make something that works for at least 90% of my visitors. The same goes for anything other than HTML5: Flash, Java, Javascript, Window-Size, etc.
Now if you do not have visitor stats, you should research your market. What kind of visitors do you want? What types of devices and do they use? And what broswers and versions are available on those devices?
Eventually those semantic tags may be used for more intelligent parsing and crawling of web-pages but AFAIK, it has yet to happen. So if they make sense to you and your intended visitors are able to see them, you can use them but at this point no one can say there is a necessity to do so.
What is left is to compare the advantage of future benefits of those tags compared to the visitors lost because they cannot see your website properly.
