Let's rephrase your question a bit before I try to answer it.
"Can I create a class in Execute Anonymous, skip creating a test class & running all test classes to get test class coverage, and then run a Schedulable class that call methods from it to use it's objects?"
I hope I've paraphrased your question reasonably well.
When one runs code using Execute Anonymous, new code only exists during the execution context of the operation. It doesn't persist and isn't intended to persist.
Allowing you to create a Class that persisted beyond the execution context of the running code would be counter to the purposes of Execute Anonymous. It would allow you to completely bypass the security integrity of the platform. If a class doesn't exist in the code base that's been compiled when a scheduled code is run "in the future" (as in at a different time than the current execution context), it won't exist in the org to be called from a schedulable class.
If you were permitted to do this, you could create any kind of malicious code and schedule it to run in system mode on a periodic basis that would hardly leave a trace of the actual code that ran. To me, this would be the equivalent of allowing someone to set a virus loose to run inside an org!
As an example, one could easily create code in a class to delete the last 10 accounts accessed, it's related opportunities, related contacts and other related records according to when the "anonymous class" is scheduled to run. The code for the class that does this wouldn't be visible for inspection. Only the schedulable that calls it would be visible in the code base. There'd be no test method and no running user. The security exposure would be enormous!