Well yeah, kind of.
You could copy a kit from one project to another using sysex or you can:
In the LOAD KIT menu, highlight a kit, hit function+rec.
load other project, goto LOAD KIT men, hit function+stop.
This was suggested by Void in this thread: Copy kits in between projects
However if your kit sounds uses samples you need to make sure you have those in the project memory slots in the new project.
A kind of good thread discussing this problem is this one: Moving Kits - Project Management
At the end of the day a project in the AR is quite isolated from other projects and moving sounds, kits and samples between projects is kind of complicated to do. This is especially true when it comes to how sounds and kits are using samples.
The upside of this compexity is that you get to learn how sounds, kits, projects, patterns relate to each other and how they relate to sample slots (the project sample RAM) etc. 