Did Ancient Romans ever consider conquering China? If they had attempted it, would they have succeeded?

To your first question

• No
• The romans were not stupid, they knew China was too far away. To be honest they did not know the precise location of China. The romans could not even conquer parthia/ persia let alone china
• Romans had no conflict of interest with chinese, and in fact romans benefited from trade with china via the silk road. There was no reason to conquer a distant major trade partner
• 

To your second question

• No as well
• As mentioned before, Romans could not fully subjugate parthia or persia, let alone china which was thousands of kilometers further away
• China by then was ruled by the powerful han dynasty, and Romans would definitely struggle to conquer such as a powerful empire with huge population, strong economy and battle hardened army
• The sheer distance, logistic and supply issue would also stop the Romans before reaching the door step of China
• Romans would not even reach India, let alone China.