Yes – this can still be done.

Yes your company can give you a credit card even if you have bad credit however It is up to them if they want to give you a company credit card. The credit card wont show up on your credit report as it is a business credit card through their credit.

Accept the job.

Think about it, If this were an issue, they most likely would not hire you in the first place.

They can, but as you pointed out, they may not want to.