Yes. Projects are saved on your hard drive. Once you purchase a MAXQDA license you can unlock your demo with a serial number and continue to work on your projects with MAXQDA Standard, Plus or Analytics Pro. You may also move your project to a different computer which has MAXQDA installed on it and continue working from there.
MAXQDA Base can only open projects that were created with MAXQDA Base. It is therefore not possible to continue a project that was created with the demo version in MAXQDA Base. The demo version is MAXQDA Analytics Pro.
The demo version contains all of the features of MAXQDA Analytics Pro. If you purchase a different MAXQDA product, some features will not be available. Please check the features comparison for more information.