This is the 100% guaranteed method to see whether you're banned or not. People will lie to themselves in hopes that their accounts will be restored. But this is the truth; you should've expected it.
Step 1:
Go to
The Official Pokemon Website | Pokemon.com
Put any random-ass date and click "Continue".
Step 2:
Ignore all the Username/Password/Email text-fields and scroll down to "Screen Name".
Step 3:
Type in the Screen Name of the account that you suspect of being banned and click "Check Availability".
Conclusion:
If it says
"This screen name already exists." then you're most likely not banned. Yet. However, if it says
"This screen name is available." then you're banned. No way around it. As a last option, I would suggest going ahead and submitting a ban appeal. Link for the form is
Pokemon GO
Cheers, Niantic.