From their license statement, it appears that the free trial period license does not permit you to make a final executable (which is a requirement of participating in the GMTK game jam). So no, you would need to purchase a full version of the editor in order to use it, to my understanding.

As an alternative, you could try out Godot Engine. It's completely free and open source, is honestly a lot better than GMS2 (and gradually approaching the quality of Unity/Unreal, though still has a lot of work to do to get there), and even includes visual scripting if you wanna go that route (though the official step-by-step tutorial series uses GDScript, a C++-Python hybrid that is tightly integrated with the engine and *extremely* easy to use and build content with. Like GMS2, it has a dedicated 2D editor, but is also a lot more flexible and powerful. Supports GDScript, VisualScript, C#, and, if you know what you are doing, at least a dozen other languages.

Full Disclosure: I'm a Godot contributor.