Any time the other driver is at fault in causing the accident--that is, was driving carelessly or negligently and caused the accident in that way--the driver who suffered injuries or property damage in the accident can sue the at-fault driver for any and all costs logically and provably coming out of the accident which were not paid by insurance, which would include your insurance deductible. You can do this whether or not the license was suspended. So yes, you have the right to sue the other driver for your deductible or other unreimbursed losses.