If I drop off a stray dog that I can not hold onto for any longer, if for any reason they schedule him to be euthanized, would they be able to notify me before hand and let me pick him back up??

No once it's given up its gone. So i suggest going back after a month to make sure it hasn't been euthanized

I've tried calling Bradshaw shelter and there is no way to get a hold of someone unless you go in

Your best bet is to call the shelter and ask that specific question.

No. If you surrender your dog, that's it. Abd since they are so overcrowded, euthanasia is a distinct possibility.

I am not an employee; however, from personal experience, the answer is no.