Usually no. Even if you have a cheap web hosting company host your web site, you will undoubtedly usually have significantly more resources with a shared hosting plan cheap web host as opposed to opting for a free web host.

Free web hosts often have very limited disk storage space allotments. For instance free web hosting often only allows for 50MB to 200MB and sometimes far less for storage. This fills extremely fast given modern day graphics, pictures, computer screen resolutions and so forth. These graphics need to be displayed on the web site so thus it is hard to have a web site with lots of graphics on a free hosting account.

Often times, free web hosting companies have thousands of accounts on 1 server which often make them run slower as well. However, if your site is extremely simple with little to no images and you don't have a significant database and you have a very small and static web site, then you may probably be able to get away with having a free web hosting account.