Yes, more or less. We can say English /ɪ/ is something between the Polish y and Polish i sounds.
For us it is a very natural sound and when we don't know what to say we often say "yyy". It is also the sound that is produced when you try to pronounce consonants without pronouncing vovels. I don't know if English speakers are the case but if you ask Zbyszek to say p /p/ or m /m/ he will surely smuggle a little and shy y: /p(y)/, /m(y).
It is similar to the central vowel (shwa) but it doesn't have this e and a tone in it. It is just pure y, I don't know how to explain it, hehehe.
Practice makes perfect.
PS. It is not /ʒ/ (like in garage), there should be a dental /z/ in your transcription.