Does aspirating voiceless stop consonants at the beginning of words matter in spoken English?

[Zoli]

The voiceless stop consonants "p", "t", and "k" are aspirated in English at the beginning of stressed words. Am I right? The words "turn" and "too" in the examples below.
As a learner, not respecting the rule can make me sound less natural in English? I would be grateful for any suggestion. Thank you so much!

 

[5jj]

Failure to aspirate can make the voiceless sounds sound a little like the voiced equivalent to native speakers. You will still be understood, but you will not sound natural.