No brother, this is not correct actually, let me explain why it's wrong.

1. Bhagwan Ram is not free from Karma he faces consequences of Karma, he himself said it see Ramayana(3.63.4) https://twitter.com/Go_Movie_Mango/status/1195224646100176896

पूर्वं मया नूनमभीप्सितानि पापानि कर्माण्यसकृत्कृतानि।तत्रायमद्यापतितो विपाको दुःखेन दुःखं यदहं विशामि। (3.63.4)

I have certainly done some Sinful Karma in past years to consequences of those I am facing sorrow after sorrow.

It means Avatar is not above Karma

Further Ramayana 2.20.29

चतुर्दश हि वर्षाणि वत्स्यामि विजने वने।
मधुमूलफलैर्जीवन्हित्वा मुनिवदामिषम्।

It just means that Sri Ram says I will not eat meat, it do not mean he used to eat meat before going to forest. https://twitter.com/Go_Movie_Mango/status/1195224653482123271?s=19

Also in Ramayana 4.17.38

It is Vali who said these words no Sri Ram or any learned person, Vali said in the same context when he was criticizing Shree Ram and calling him Sinful and Adharmic etc. https://twitter.com/Go_Movie_Mango/status/1196295099635945472?s=19