Mlecchas are those who live outside Bharata Varsha. As they live outside India, they don't have any Varna and they should be considered as lower than all Varnas. But if a Mleccha convert to Hinduism, considering the story written here in Bhavishya Purana, can he become a dvija or a Shudra?
The story written there is:
Then the sage went to the country known as Misra and put all the mlecchas into illusion by the greace of goddess Sarasvati.
Then he made 10,000 people as dvijas or twice born brahmanas; he made 2,000 people into vaishyas; and the rest of them as shudras. He came back with them and staying in Arya-desha (India) he engaged in the activites of the sages. They were known as Aryans and by the grace of goddess Sarasvati their generation gradually increased upto 4 million, both the men and women with their sons and grandsons. Their king, Kasyapa muni, ruled the earth for 120 years.