So, if a molecule does not have a chiral centre, then can it and the mirror image superimpose on each other?
No. By definition they are non-superimposable. Not all asymmetric centers are caused from 4 unique groups (sp
3 hydridization). There are compounds in which the center you are looking at may not have 4 unique groups but it can still be chiral.
Don't worry about this though.
By four unique groups I mean, by example, the boldface sp
3 carbon in the following:
CH
3CH
2CH(OH)NH
2