I don't know for sure but I am thinking that deleting songs on your phone will not affect your ability to get them again via Itunes. Those songs are likely 'owned' by your account.
I am only saying this because I purchased a handful of songs on Itunes many years ago and I still see them there in Itunes even though I lost interest in Apple as a music source when I switched to Spotify. I for sure had those songs on one of my Iphones and I would have wiped and reset my Iphone for recycling. Doing that did not affect my Itunes library it seems.