You may do. If asked the question regarding convictions, you should be honest and Frank with the Mexican authorities.
I hope this answers your questions. If so, kindly rate the answer and provide feedback.
If you have any further questions, please do not hesitate to ask.
I am not sure if they do is the honest answer.
The only way to check for sure is to apply for a visa to the Mexican embassy.
Yes you could be sent home.
A visa would ensure that you have disclosed all of the relevant information. If the authorities are satisfied, a visa would be issued. If not, it would be refused.
At least you won't be sent home from the port of entry.