According to the scriptures, is there any mention of whether complete pure souls can exist in Kali Yuga?
Yes, of course.
There are many sloksa in different Puranas mentioning that Chanting of the Name of God removes all sins and makes a man pure. I am quoting one from the Garuda-Purana
Kalau sankirtanaad eva sarvam paapam vyaapohati, meaning that Nama-Sankitrtana alone removes all sins in the age of kali (Reference: Omkarnath Rachanavali, Mahamilan Math,vol 1, page 318).
So many saints like Sri Chaitanya and His disciples, Nanak, Kavir,Tulsidas, Dadu, Meerabai etc took birth in the kali-yuga! I feel their characters are as glorious as the great characters of our scriptures or of people in the Satya Yuga, if ofttimes not more, (excluding incarnations like Sri Rama and Sri Krishna of course.)