To detect whether a user has an AdWords account, log in as that user and request the accounts the user has access to. If you get one or more accounts, apparently something is present. Otherwise (0 accounts, or an error like NOT_ADS_USER), the user has no access to any AdWords account.
To find out which accounts a user has access to, use CustomerService.get() and/or ManagedCustomerService.get().
Hope this helps.