Yes, you can get any character in the lower gens vs higher gens.
Two things influence the character you will get:
1. Odd vs Even gen. number (some are only odd gen, some only even gen)
2. The way you care for it whilst it is growing (How full the happy / hungry hearts are kept, how many training points you get as it is growing up, etc.)
So you have as good a chance at getting a rare character in an early gen as you do in a higher gen....
Best, etc.
TamaMum