I was recently diagnosed with having a left atrial abnormality and a left bundle branch Blockage, I really need to have a lot of dental work done plus I will need to be put to sleep with this problem, can I be put to sleep?

This is a question that can only be answered by both the physician and the dentist, who know your entire history, not just this one diagnosis.
Not all dentists will put patients to sleep - have you asked? If so, the dentist needs to confer with the doctor.

You normally will go to a dental surgical office. Most "dentist" at least here in Atlanta don't even pull a tooth any more, they send you to a dental surgical office for that.

But patients are put to sleep for all types of dental work, it is all a matter of what you can afford to pay for.