No.
2 years old is not too old for wearing diapers.
A lot of 2 year old kids wear diapers full time because some 2 year olds are not potty trained because they are not ready to be toilet trained.
Some 2 year olds may be ready to potty train and stop wearing diapers and some may not be.
For some kids they are potty trained and out of diapers by age 18 months of age and some are not ready until 2 or 3 years of age.
There's no real age limit on wearing diapers but a child should be potty trained by 4 years old as long as they have no other health issues.
I have a 2 year old son and 2 year old nephew who are both still wearing diapers all day and night because they are not ready to toilet train.
The kids will usually potty train on their own by age 4 but if not then you should push the issue.
I also sometimes babysit a 3 year old boy who is not potty trained and he's still wearing diapers and that's okay as well.