No, there is always a difference in vowel length - pay attention to the accent (čárka)! The third person plural ("they") ending is usually -í/-ejí/-ou depending on the verb class. On the other hand, first person singular ("I") ending is usually - i/-ím/-u depending on the verb class.
Is there a clear difference between "vejce" and "vajíčko"? In the link below they say that both are commonly used, but someone also mentioned that there is a size distinction (since etymologically "vajíčko" is the diminutive of "vejce"). I'd like to know what your opinions are about when to use either.
Edit: found that this question had been answered just after I posted it: https://forum.duolingo.com/comment/24725809