Hi, my name is XXXXX XXXXX I have been in the home improvement and repair field for 20 years. I will be glad to help you today. You could do that but you are taking a great chance. It is better that you do not. If the old flooring is not perfectly glued then then it will likely come up later. The best is to get it down to the sub floor and start new.
You could always put 1/4" plywood down first and an underlayment. That would take care of the issues with the flooring coming up and any imperfections coming through.