Thanks for your question.
The UKBA are permitted to take "Good Character" in to account when decided all application now, it's not just for ILR/Naturalisation applications. They can refuse if they consider a person not to be of good character, so (in theory) yes they could refuse.
It is at the discretion of the UKBA whether to refuse on the basis of the conviction. You have to disclose the conviction otherwise you would be deceiving the UKBA which would be more serious than the conviction itself. You have to then mitigate the disclosure by stating how you have rehabilitated yourself since the conviction.
It is worth applying but by doing so you must acknowledge that the application is more complicated and has a higher possible chance of refusal because of the conviction. If you adequately mitigate then you should be okay (assuming there are no other defects with your application
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