Is it possible that a high tolerance for alcohol will cause prescription pain killers to not be very effective?

Yes. There is a similarity in how the brain handles alcohol, tranquilizers, and pain medications; high tolerance to one is often associated with high tolerance for others.
It depends. Tolerance to alcohol and opioids don't overlap. I would wonder if you have something like sleep apnea, which made worse by alcohol, would contribute to the opioids not working as well. Also, alcohol can be toxic to the brain, & interfere ith sleep, all of which are not good for good pain management. Mixing opiods and pain pills dangerous. Time to get help stopping alcohol.