By default, when you import data into Fusion 360 the timeline is disabled. If you enable timeline, the existing sketches, surfaces, or bodies are going to be available in Direct Modeling mode. You might think of this in a similar way to how Inventor would import a STEP file as a "Dumb Solid" (with no native features).
If you are looking to utilize parameters to update the model (from within the parameters dialog), you will need to create the features outside of these Base Feature. The below youtube video shows how you can create features and dimensions that can be update parametrically.
http://www.youtube.com/watch?v=apkUQKNwHIo
For your sketches that are being imported in, is the goal to be able to modify these sketches in a similar fashion to the youtube video where you edit the value of a parameter?
If yes, then you will need to create these sketches with dimensions while not in a base feature. You can copy and paste sketch entities. If you copy and paste, please note that you have to copy while editing the imported sketches and paste during the creation of a new sketch (with capture history enabled). One useful hint may be to use the "Move to Sketch Plane" command from the right click menu while selecting sketch entities.
You could also project the sketch entities as you mentioned. If you use the project, you can right click on the sketch entities and choose break link to begin to add dimension to the figures.
If you don't really need the parameters, and are just looking to take advantage of the timeline for updating the model, you may consider building features outside of the base feature with the existing imported sketches. Downstream commands will update as the timeline computes each feature.
I hope that helps. Let me know if anything is unclear or if you have any questions.
Kind Regards,
Nathan Chandler
Principal Specialist