If you are ineligible for a bonus and have claimed the maximum amount of bonuses according to the operators' rules, you will either not be allowed to create an account or simply be unable to claim a bonus.
If you have created an account and realised that you cannot claim the bonus, you will not be able to stop the initial deposit, however, you should be able to withdraw the funds at any time as they are not beholden to bonus T&Cs, although players should check before signing up.