It is really a decision for the FSA to rule on, and they tend to view things on a case by case basis. I do have clients who are FSA regulated, and so long as you are demonstrating a responsibility to resolving your debts, there seems no reason why they would not allow you to continue to be authorised.
It depends on the role you will play in the regulated firm, and whether financial pressures could cause you to give advice because it would benefit you financially, rather than benefit the client. Another big factor is whether your employer will make a good case for you. The FSA will say that it is up to the firm who take compliance responsibility for you to decide. They must be sure they can strongly defend any future challenge from the FSA on this decision. Often it comes down to whether the firm will take the risk or not.
What type of firm are you considering joining, are they directly authoreised or an appointed representative, and what will your role and job responsibilities be within that firm ?