It is possible, but it typically winds up wasting a small amount of physical memory.
When your system starts up, a lot of processes run that handle things like system services. Many of these processes dirty pages of memory that they will never access again for the entire life of the system. With no page file, these pages remain in physical memory for the entire time the system is running. With a page file, these pages will be copied to the page file as soon as the system hits any memory pressure, and the physical memory will be made free again. (The system can't just discard the pages because it can't prove they will never be accessed.)
You can measure how much memory this is by running the system with a page file, using it normally for an hour or so, and seeing how much page file space is used.
If you have significantly more physical memory that the system's working set is ever likely to be, this is insignificant and you can run with no page file.
On UNIX machines, there are other issues with
fork and overcommitting physical memory, but they don't apply on Windows.