Absolutely. And it WILL cycle, regardless on if you're doing it intentionally or not, it's part of the "life" of a tank. Having established media in the filter will help it along quite a bit though. I would think that with the pre-loaded media, and that level, you're ok for now for a "safe" fishy cycle, but watch your parameters and make sure to monitor with a slow build.
Are my fish safe in the new tank
Are my fish safe in the new tank
Yes the fish are the same and the filters are the same and also driftwood and decos are the same